id sid tid token lemma pos cana-5883 1 1 communications communication NOUN cana-5883 1 2 on on ADP cana-5883 1 3 applied apply VERB cana-5883 1 4 nonlinear nonlinear ADJ cana-5883 1 5 analysis analysis NOUN cana-5883 1 6 issn issn NOUN cana-5883 1 7 : : PUNCT cana-5883 1 8 1074 1074 NUM cana-5883 1 9 - - PUNCT cana-5883 1 10 133x 133x NUM cana-5883 1 11 vol vol NOUN cana-5883 1 12 32 32 NUM cana-5883 1 13 no no NOUN cana-5883 1 14 . . PUNCT cana-5883 2 1 2s 2s NUM cana-5883 2 2 ( ( PUNCT cana-5883 2 3 2025 2025 NUM cana-5883 2 4 ) ) PUNCT cana-5883 2 5 604 604 NUM cana-5883 2 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 2 7 bianchi bianchi NOUN cana-5883 2 8 type type NOUN cana-5883 2 9 v v NOUN cana-5883 2 10 universe universe NOUN cana-5883 2 11 with with ADP cana-5883 2 12 qvdp qvdp PROPN cana-5883 2 13 in in ADP cana-5883 2 14 f f PROPN cana-5883 2 15 ( ( PUNCT cana-5883 2 16 r r PROPN cana-5883 2 17 , , PUNCT cana-5883 2 18 t t NOUN cana-5883 2 19 ) ) PUNCT cana-5883 2 20 theory theory NOUN cana-5883 2 21 of of ADP cana-5883 2 22 gravity gravity NOUN cana-5883 2 23 vandana vandana PROPN cana-5883 2 24 soni1 soni1 PROPN cana-5883 2 25 & & CCONJ cana-5883 2 26 sudha sudha PROPN cana-5883 2 27 agrawal2 agrawal2 PROPN cana-5883 3 1 1department 1department NUM cana-5883 3 2 of of ADP cana-5883 3 3 mathematics mathematic NOUN cana-5883 3 4 , , PUNCT cana-5883 3 5 aks aks PROPN cana-5883 3 6 university university NOUN cana-5883 3 7 , , PUNCT cana-5883 3 8 satna-485001 satna-485001 ADJ cana-5883 3 9 , , PUNCT cana-5883 3 10 ( ( PUNCT cana-5883 3 11 m.p m.p PROPN cana-5883 3 12 . . PROPN cana-5883 3 13 ) ) PUNCT cana-5883 4 1 , , PUNCT cana-5883 4 2 india india PROPN cana-5883 4 3 sonivandana06@gmail.com sonivandana06@gmail.com PROPN cana-5883 4 4 2department 2department NUM cana-5883 4 5 of of ADP cana-5883 4 6 mathematics mathematic NOUN cana-5883 4 7 , , PUNCT cana-5883 4 8 aks aks PROPN cana-5883 4 9 university university NOUN cana-5883 4 10 , , PUNCT cana-5883 4 11 -485001 -485001 PROPN cana-5883 4 12 , , PUNCT cana-5883 4 13 ( ( PUNCT cana-5883 4 14 m.p m.p PROPN cana-5883 4 15 . . PROPN cana-5883 4 16 ) ) PUNCT cana-5883 4 17 , , PUNCT cana-5883 4 18 india india PROPN cana-5883 4 19 corresponding corresponding PROPN cana-5883 4 20 author author NOUN cana-5883 4 21 : : PUNCT cana-5883 4 22 sudha.agrawal10@gmail.com sudha.agrawal10@gmail.com X cana-5883 4 23 article article NOUN cana-5883 4 24 history history NOUN cana-5883 4 25 : : PUNCT cana-5883 4 26 received receive VERB cana-5883 4 27 : : PUNCT cana-5883 4 28 04 04 NUM cana-5883 4 29 - - PUNCT cana-5883 4 30 01 01 NUM cana-5883 4 31 - - PUNCT cana-5883 4 32 2025 2025 NUM cana-5883 4 33 revised revise VERB cana-5883 4 34 : : PUNCT cana-5883 4 35 25 25 NUM cana-5883 4 36 - - PUNCT cana-5883 4 37 01 01 NUM cana-5883 4 38 - - PUNCT cana-5883 4 39 2025 2025 NUM cana-5883 4 40 accepted accept VERB cana-5883 4 41 : : PUNCT cana-5883 4 42 21 21 NUM cana-5883 4 43 - - SYM cana-5883 4 44 02 02 NUM cana-5883 4 45 - - PUNCT cana-5883 4 46 2025 2025 NUM cana-5883 4 47 abstract abstract NOUN cana-5883 4 48 : : PUNCT cana-5883 4 49 throughout throughout ADP cana-5883 4 50 the the DET cana-5883 4 51 report report NOUN cana-5883 4 52 , , PUNCT cana-5883 4 53 the the DET cana-5883 4 54 bianchi bianchi NOUN cana-5883 4 55 cosmological cosmological ADJ cana-5883 4 56 model model NOUN cana-5883 4 57 is be AUX cana-5883 4 58 contemplating contemplate VERB cana-5883 4 59 within within ADP cana-5883 4 60 a a DET cana-5883 4 61 context context NOUN cana-5883 4 62 of of ADP cana-5883 4 63 f f PROPN cana-5883 4 64 ( ( PUNCT cana-5883 4 65 r r PROPN cana-5883 4 66 , , PUNCT cana-5883 4 67 t t NOUN cana-5883 4 68 ) ) PUNCT cana-5883 4 69 gravity gravity NOUN cana-5883 4 70 . . PUNCT cana-5883 5 1 under under ADP cana-5883 5 2 the the DET cana-5883 5 3 recently recently ADV cana-5883 5 4 proposed propose VERB cana-5883 5 5 the the DET cana-5883 5 6 deceleration deceleration NOUN cana-5883 5 7 parameter parameter NOUN cana-5883 5 8 in in ADP cana-5883 5 9 quadratic quadratic ADJ cana-5883 5 10 form form NOUN cana-5883 5 11 , , PUNCT cana-5883 5 12 the the DET cana-5883 5 13 solutions solution NOUN cana-5883 5 14 to to ADP cana-5883 5 15 the the DET cana-5883 5 16 reconditioned recondition VERB cana-5883 5 17 field field NOUN cana-5883 5 18 equations equation NOUN cana-5883 5 19 have have AUX cana-5883 5 20 been be AUX cana-5883 5 21 found find VERB cana-5883 5 22 by by ADP cana-5883 5 23 bakery bakery NOUN cana-5883 5 24 and and CCONJ cana-5883 5 25 shafeek shafeek PROPN cana-5883 5 26 ( ( PUNCT cana-5883 5 27 2019 2019 NUM cana-5883 5 28 ) ) PUNCT cana-5883 5 29 . . PUNCT cana-5883 6 1 big big ADJ cana-5883 6 2 explosion explosion NOUN cana-5883 6 3 uniqueness uniqueness NOUN cana-5883 6 4 at at ADP cana-5883 6 5 infinite infinite ADJ cana-5883 6 6 time time NOUN cana-5883 6 7 t t PROPN cana-5883 6 8 = = SYM cana-5883 6 9 0 0 PUNCT cana-5883 6 10 and and CCONJ cana-5883 6 11 shred shre VERB cana-5883 6 12 with with ADP cana-5883 6 13 respect respect NOUN cana-5883 6 14 to to ADP cana-5883 6 15 t t NOUN cana-5883 6 16 = = SYM cana-5883 6 17 1 1 NUM cana-5883 6 18 are be AUX cana-5883 6 19 expose expose VERB cana-5883 6 20 to to PART cana-5883 6 21 view view VERB cana-5883 6 22 by by ADP cana-5883 6 23 the the DET cana-5883 6 24 model model NOUN cana-5883 6 25 . . PUNCT cana-5883 7 1 studies study NOUN cana-5883 7 2 have have AUX cana-5883 7 3 been be AUX cana-5883 7 4 accompanied accompany VERB cana-5883 7 5 on on ADP cana-5883 7 6 the the DET cana-5883 7 7 development development NOUN cana-5883 7 8 of of ADP cana-5883 7 9 the the DET cana-5883 7 10 universe universe NOUN cana-5883 7 11 . . PUNCT cana-5883 8 1 physical physical ADJ cana-5883 8 2 and and CCONJ cana-5883 8 3 dynamical dynamical ADJ cana-5883 8 4 properties property NOUN cana-5883 8 5 and and CCONJ cana-5883 8 6 a a DET cana-5883 8 7 graphical graphical ADJ cana-5883 8 8 depiction depiction NOUN cana-5883 8 9 has have AUX cana-5883 8 10 also also ADV cana-5883 8 11 been be AUX cana-5883 8 12 provided provide VERB cana-5883 8 13 . . PUNCT cana-5883 9 1 typical typical ADJ cana-5883 9 2 parameter parameter NOUN cana-5883 9 3 of of ADP cana-5883 9 4 field field NOUN cana-5883 9 5 equations equation NOUN cana-5883 9 6 is be AUX cana-5883 9 7 determined determine VERB cana-5883 9 8 also also ADV cana-5883 9 9 we we PRON cana-5883 9 10 discussed discuss VERB cana-5883 9 11 the the DET cana-5883 9 12 jerk jerk NOUN cana-5883 9 13 parameter parameter NOUN cana-5883 9 14 of of ADP cana-5883 9 15 the the DET cana-5883 9 16 proposed propose VERB cana-5883 9 17 model model NOUN cana-5883 9 18 . . PUNCT cana-5883 10 1 key key ADJ cana-5883 10 2 words word NOUN cana-5883 10 3 : : PUNCT cana-5883 10 4 f f PROPN cana-5883 10 5 ( ( PUNCT cana-5883 10 6 r r NOUN cana-5883 10 7 , , PUNCT cana-5883 10 8 t t NOUN cana-5883 10 9 ) ) PUNCT cana-5883 10 10 theory theory NOUN cana-5883 10 11 of of ADP cana-5883 10 12 gravity gravity NOUN cana-5883 10 13 , , PUNCT cana-5883 10 14 b b X cana-5883 10 15 - - PUNCT cana-5883 10 16 v v NOUN cana-5883 10 17 galactic galactic ADJ cana-5883 10 18 model model NOUN cana-5883 10 19 , , PUNCT cana-5883 10 20 deceleration deceleration NOUN cana-5883 10 21 parameter parameter NOUN cana-5883 10 22 , , PUNCT cana-5883 10 23 state state NOUN cana-5883 10 24 finder finder PROPN cana-5883 10 25 parameter parameter PROPN cana-5883 10 26 . . PUNCT cana-5883 11 1 i. i. PROPN cana-5883 11 2 introduction introduction NOUN cana-5883 11 3 according accord VERB cana-5883 11 4 to to ADP cana-5883 11 5 the the DET cana-5883 11 6 discussion discussion NOUN cana-5883 11 7 on on ADP cana-5883 11 8 many many ADJ cana-5883 11 9 observations observation NOUN cana-5883 11 10 by by ADP cana-5883 11 11 many many ADJ cana-5883 11 12 researchers researcher NOUN cana-5883 11 13 , , PUNCT cana-5883 11 14 the the DET cana-5883 11 15 cause cause NOUN cana-5883 11 16 of of ADP cana-5883 11 17 the the DET cana-5883 11 18 accelerated accelerate VERB cana-5883 11 19 universe universe NOUN cana-5883 11 20 is be AUX cana-5883 11 21 dark dark ADJ cana-5883 11 22 energy energy NOUN cana-5883 11 23 is be AUX cana-5883 11 24 most most ADV cana-5883 11 25 responsible responsible ADJ cana-5883 11 26 candidate candidate NOUN cana-5883 11 27 . . PUNCT cana-5883 12 1 sinister sinister ADJ cana-5883 12 2 energy energy NOUN cana-5883 12 3 to to PART cana-5883 12 4 be be AUX cana-5883 12 5 contemplate contemplate ADJ cana-5883 12 6 as as ADP cana-5883 12 7 a a DET cana-5883 12 8 substance substance NOUN cana-5883 12 9 with with ADP cana-5883 12 10 under under ADP cana-5883 12 11 pressure pressure NOUN cana-5883 12 12 which which PRON cana-5883 12 13 influence influence NOUN cana-5883 12 14 the the DET cana-5883 12 15 current current ADJ cana-5883 12 16 cosmological cosmological ADJ cana-5883 12 17 energy energy NOUN cana-5883 12 18 movement movement NOUN cana-5883 12 19 . . PUNCT cana-5883 13 1 by by ADP cana-5883 13 2 various various ADJ cana-5883 13 3 observations observation NOUN cana-5883 13 4 , , PUNCT cana-5883 13 5 it it PRON cana-5883 13 6 becomes become VERB cana-5883 13 7 necessary necessary ADJ cana-5883 13 8 to to PART cana-5883 13 9 envision envision VERB cana-5883 13 10 and and CCONJ cana-5883 13 11 concede concede VERB cana-5883 13 12 the the DET cana-5883 13 13 nature nature NOUN cana-5883 13 14 of of ADP cana-5883 13 15 force force NOUN cana-5883 13 16 field field NOUN cana-5883 14 1 [ [ X cana-5883 14 2 1 1 NUM cana-5883 14 3 - - SYM cana-5883 14 4 4 4 NUM cana-5883 14 5 ] ] PUNCT cana-5883 14 6 . . PUNCT cana-5883 15 1 among among ADP cana-5883 15 2 the the DET cana-5883 15 3 most most ADV cana-5883 15 4 broadly broadly ADV cana-5883 15 5 considered consider VERB cana-5883 15 6 claimant claimant NOUN cana-5883 15 7 of of ADP cana-5883 15 8 dark dark ADJ cana-5883 15 9 energy energy NOUN cana-5883 15 10 is be AUX cana-5883 15 11 the the DET cana-5883 15 12 empty empty ADJ cana-5883 15 13 space space NOUN cana-5883 15 14 of of ADP cana-5883 15 15 the the DET cana-5883 15 16 cosmological cosmological ADJ cana-5883 15 17 constant constant ADJ cana-5883 15 18 Ξ» Ξ» NOUN cana-5883 15 19 . . PUNCT cana-5883 16 1 but but CCONJ cana-5883 16 2 in in ADP cana-5883 16 3 cosmology cosmology NOUN cana-5883 16 4 , , PUNCT cana-5883 16 5 it it PRON cana-5883 16 6 brawls brawl VERB cana-5883 16 7 with with ADP cana-5883 16 8 remarkable remarkable ADJ cana-5883 16 9 problems problem NOUN cana-5883 16 10 among among ADP cana-5883 16 11 them they PRON cana-5883 16 12 like like ADP cana-5883 16 13 cosmic cosmic ADJ cana-5883 16 14 coincidence coincidence NOUN cana-5883 16 15 and and CCONJ cana-5883 16 16 fine fine ADJ cana-5883 16 17 tuning tuning NOUN cana-5883 16 18 [ [ X cana-5883 16 19 5 5 NUM cana-5883 16 20 - - SYM cana-5883 16 21 7 7 NUM cana-5883 16 22 ] ] PUNCT cana-5883 16 23 . . PUNCT cana-5883 17 1 some some DET cana-5883 17 2 other other ADJ cana-5883 17 3 features feature NOUN cana-5883 17 4 of of ADP cana-5883 17 5 dark dark ADJ cana-5883 17 6 energy energy NOUN cana-5883 17 7 are be AUX cana-5883 17 8 chaplygin chaplygin ADJ cana-5883 17 9 gas gas NOUN cana-5883 17 10 ( ( PUNCT cana-5883 17 11 a a DET cana-5883 17 12 dark dark ADJ cana-5883 17 13 fluid fluid NOUN cana-5883 17 14 which which PRON cana-5883 17 15 might might AUX cana-5883 17 16 describe describe VERB cana-5883 17 17 the the DET cana-5883 17 18 past past ADJ cana-5883 17 19 decelerating decelerating NOUN cana-5883 17 20 matter matter NOUN cana-5883 17 21 dominated dominate VERB cana-5883 17 22 era era NOUN cana-5883 17 23 and and CCONJ cana-5883 17 24 at at ADP cana-5883 17 25 present present ADJ cana-5883 17 26 time time NOUN cana-5883 17 27 it it PRON cana-5883 17 28 provides provide VERB cana-5883 17 29 an an DET cana-5883 17 30 accelerating accelerate VERB cana-5883 17 31 expansion expansion NOUN cana-5883 17 32 of of ADP cana-5883 17 33 the the DET cana-5883 17 34 universe universe NOUN cana-5883 17 35 . . PUNCT cana-5883 17 36 ) ) PUNCT cana-5883 18 1 [ [ X cana-5883 18 2 8 8 NUM cana-5883 18 3 ] ] PUNCT cana-5883 18 4 , , PUNCT cana-5883 18 5 tachyons tachyon NOUN cana-5883 18 6 ( ( PUNCT cana-5883 18 7 a a DET cana-5883 18 8 hypothetical hypothetical ADJ cana-5883 18 9 particle particle NOUN cana-5883 18 10 that that PRON cana-5883 18 11 travels travel VERB cana-5883 18 12 faster fast ADV cana-5883 18 13 than than ADP cana-5883 18 14 the the DET cana-5883 18 15 speed speed NOUN cana-5883 18 16 of of ADP cana-5883 18 17 light light NOUN cana-5883 18 18 . . PUNCT cana-5883 18 19 ) ) PUNCT cana-5883 19 1 [ [ X cana-5883 19 2 9 9 NUM cana-5883 19 3 ] ] PUNCT cana-5883 19 4 , , PUNCT cana-5883 19 5 quintessence quintessence NOUN cana-5883 19 6 ( ( PUNCT cana-5883 19 7 bottom bottom ADJ cana-5883 19 8 distillation distillation NOUN cana-5883 19 9 ) ) PUNCT cana-5883 19 10 [ [ X cana-5883 19 11 10 10 NUM cana-5883 19 12 ] ] PUNCT cana-5883 19 13 , , PUNCT cana-5883 19 14 phantom phantom NOUN cana-5883 19 15 ( ( PUNCT cana-5883 19 16 wraith wraith NOUN cana-5883 19 17 ) ) PUNCT cana-5883 20 1 [ [ X cana-5883 20 2 11 11 NUM cana-5883 20 3 ] ] PUNCT cana-5883 20 4 , , PUNCT cana-5883 20 5 k k NOUN cana-5883 20 6 - - NOUN cana-5883 20 7 essence essence NOUN cana-5883 20 8 [ [ X cana-5883 20 9 12 12 NUM cana-5883 20 10 ] ] PUNCT cana-5883 20 11 . . PUNCT cana-5883 21 1 by by AUX cana-5883 21 2 notify notify VERB cana-5883 21 3 the the DET cana-5883 21 4 angular angular ADJ cana-5883 21 5 part part NOUN cana-5883 21 6 of of ADP cana-5883 21 7 the the DET cana-5883 21 8 eh eh INTJ cana-5883 21 9 action action NOUN cana-5883 21 10 , , PUNCT cana-5883 21 11 make make VERB cana-5883 21 12 alteration alteration NOUN cana-5883 21 13 to to ADP cana-5883 21 14 gravity gravity NOUN cana-5883 21 15 theories theory NOUN cana-5883 21 16 can can AUX cana-5883 21 17 be be AUX cana-5883 21 18 acquired acquire VERB cana-5883 21 19 . . PUNCT cana-5883 22 1 these these DET cana-5883 22 2 theories theory NOUN cana-5883 22 3 have have AUX cana-5883 22 4 recently recently ADV cana-5883 22 5 leap leap VERB cana-5883 22 6 up up ADP cana-5883 22 7 to to ADP cana-5883 22 8 the the DET cana-5883 22 9 top top NOUN cana-5883 22 10 of of ADP cana-5883 22 11 the the DET cana-5883 22 12 list list NOUN cana-5883 22 13 of of ADP cana-5883 22 14 options option NOUN cana-5883 22 15 for for ADP cana-5883 22 16 clarification clarification NOUN cana-5883 22 17 the the DET cana-5883 22 18 unsolved unsolved ADJ cana-5883 22 19 problem problem NOUN cana-5883 22 20 of of ADP cana-5883 22 21 the the DET cana-5883 22 22 accelerating accelerate VERB cana-5883 22 23 phase phase NOUN cana-5883 22 24 of of ADP cana-5883 22 25 the the DET cana-5883 22 26 universe universe ADJ cana-5883 22 27 enlargement enlargement NOUN cana-5883 22 28 . . PUNCT cana-5883 23 1 the the DET cana-5883 23 2 simplest simple ADJ cana-5883 23 3 and and CCONJ cana-5883 23 4 most most ADV cana-5883 23 5 common common ADJ cana-5883 23 6 converting converting NOUN cana-5883 23 7 of of ADP cana-5883 23 8 gr gr NOUN cana-5883 23 9 in in ADP cana-5883 23 10 this this DET cana-5883 23 11 situation situation NOUN cana-5883 23 12 is be AUX cana-5883 23 13 f(r f(r NOUN cana-5883 23 14 ) ) PUNCT cana-5883 23 15 gravity gravity NOUN cana-5883 23 16 . . PUNCT cana-5883 24 1 the the DET cana-5883 24 2 f(r f(r NOUN cana-5883 24 3 ) ) PUNCT cana-5883 24 4 gravity gravity NOUN cana-5883 24 5 theory theory NOUN cana-5883 24 6 was be AUX cana-5883 24 7 first first ADV cana-5883 24 8 dispensed dispense VERB cana-5883 24 9 in in ADP cana-5883 24 10 buchdah,1970 buchdah,1970 PROPN cana-5883 24 11 [ [ X cana-5883 24 12 13 13 NUM cana-5883 24 13 ] ] PUNCT cana-5883 24 14 , , PUNCT cana-5883 24 15 and and CCONJ cana-5883 24 16 it it PRON cana-5883 24 17 was be AUX cana-5883 24 18 afterwards afterwards ADV cana-5883 24 19 utilized utilize VERB cana-5883 24 20 to to PART cana-5883 24 21 discover discover VERB cana-5883 24 22 an an DET cana-5883 24 23 isotropic isotropic NOUN cana-5883 24 24 , , PUNCT cana-5883 24 25 non non ADJ cana-5883 24 26 - - ADJ cana-5883 24 27 singular singular ADJ cana-5883 24 28 desitter desitter NOUN cana-5883 24 29 type type NOUN cana-5883 24 30 cosmological cosmological ADJ cana-5883 24 31 solutions solution NOUN cana-5883 24 32 [ [ X cana-5883 24 33 14 14 NUM cana-5883 24 34 ] ] PUNCT cana-5883 24 35 . . PUNCT cana-5883 25 1 the the DET cana-5883 25 2 masses masse NOUN cana-5883 25 3 authors author NOUN cana-5883 25 4 have have AUX cana-5883 25 5 inquired inquire VERB cana-5883 25 6 various various ADJ cana-5883 25 7 aspects aspect NOUN cana-5883 25 8 of of ADP cana-5883 25 9 𝑓(𝑅 𝑓(𝑅 NOUN cana-5883 25 10 ) ) PUNCT cana-5883 25 11 gravity gravity NOUN cana-5883 25 12 for for ADP cana-5883 25 13 different different ADJ cana-5883 25 14 type type NOUN cana-5883 25 15 cosmological cosmological ADJ cana-5883 25 16 models model NOUN cana-5883 25 17 , , PUNCT cana-5883 25 18 [ [ X cana-5883 25 19 15 15 NUM cana-5883 25 20 - - SYM cana-5883 25 21 18 18 NUM cana-5883 25 22 ] ] PUNCT cana-5883 25 23 . . PUNCT cana-5883 26 1 moreover moreover ADV cana-5883 26 2 , , PUNCT cana-5883 26 3 it it PRON cana-5883 26 4 is be AUX cana-5883 26 5 signified signify VERB cana-5883 26 6 that that SCONJ cana-5883 26 7 the the DET cana-5883 26 8 f(r f(r NOUN cana-5883 26 9 ) ) PUNCT cana-5883 26 10 gravity gravity NOUN cana-5883 26 11 is be AUX cana-5883 26 12 congenial congenial ADJ cana-5883 26 13 with with ADP cana-5883 26 14 recent recent ADJ cana-5883 26 15 observations observation NOUN cana-5883 27 1 [ [ X cana-5883 27 2 19 19 NUM cana-5883 27 3 - - SYM cana-5883 27 4 22 22 NUM cana-5883 27 5 ] ] PUNCT cana-5883 27 6 . . PUNCT cana-5883 28 1 nevertheless nevertheless ADV cana-5883 28 2 , , PUNCT cana-5883 28 3 modern modern ADJ cana-5883 28 4 cosmology cosmology NOUN cana-5883 28 5 now now ADV cana-5883 28 6 addresses address VERB cana-5883 28 7 the the DET cana-5883 28 8 anisotropy anisotropy NOUN cana-5883 28 9 problem problem NOUN cana-5883 28 10 in in ADP cana-5883 28 11 inclusion inclusion NOUN cana-5883 28 12 to to ADP cana-5883 28 13 the the DET cana-5883 28 14 dark dark ADJ cana-5883 28 15 energy energy NOUN cana-5883 28 16 problem problem NOUN cana-5883 28 17 . . PUNCT cana-5883 29 1 span span VERB cana-5883 29 2 the the DET cana-5883 29 3 latest late ADJ cana-5883 29 4 factual factual ADJ cana-5883 29 5 data datum NOUN cana-5883 29 6 supports support VERB cana-5883 29 7 the the DET cana-5883 29 8 prospect prospect NOUN cana-5883 29 9 of of ADP cana-5883 29 10 an an DET cana-5883 29 11 anisotropic anisotropic NOUN cana-5883 29 12 aspects aspect NOUN cana-5883 29 13 in in ADP cana-5883 29 14 mailto:sonivandana06@gmail.com mailto:sonivandana06@gmail.com PROPN cana-5883 29 15 mailto:sudha.agrawal10@gmail.com mailto:sudha.agrawal10@gmail.com PROPN cana-5883 29 16 communications communication NOUN cana-5883 29 17 on on ADP cana-5883 29 18 applied apply VERB cana-5883 29 19 nonlinear nonlinear ADJ cana-5883 29 20 analysis analysis NOUN cana-5883 29 21 issn issn NOUN cana-5883 29 22 : : PUNCT cana-5883 29 23 1074 1074 NUM cana-5883 29 24 - - PUNCT cana-5883 29 25 133x 133x NUM cana-5883 29 26 vol vol NOUN cana-5883 29 27 32 32 NUM cana-5883 29 28 no no NOUN cana-5883 29 29 . . PUNCT cana-5883 30 1 2s 2s NUM cana-5883 30 2 ( ( PUNCT cana-5883 30 3 2025 2025 NUM cana-5883 30 4 ) ) PUNCT cana-5883 30 5 605 605 NUM cana-5883 30 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 30 7 previous previous ADJ cana-5883 30 8 periods period NOUN cana-5883 30 9 of of ADP cana-5883 30 10 the the DET cana-5883 30 11 cosmos cosmos PROPN cana-5883 30 12 , , PUNCT cana-5883 30 13 the the DET cana-5883 30 14 frw frw PROPN cana-5883 30 15 models model NOUN cana-5883 30 16 deduce deduce VERB cana-5883 30 17 the the DET cana-5883 30 18 nature nature NOUN cana-5883 30 19 of of ADP cana-5883 30 20 the the DET cana-5883 30 21 modern modern ADJ cana-5883 30 22 universe universe NOUN cana-5883 30 23 as as ADP cana-5883 30 24 spatially spatially ADV cana-5883 30 25 uniform uniform NOUN cana-5883 30 26 and and CCONJ cana-5883 30 27 isotropic isotropic NOUN cana-5883 30 28 [ [ X cana-5883 30 29 23 23 NUM cana-5883 30 30 ] ] PUNCT cana-5883 30 31 . . PUNCT cana-5883 31 1 this this DET cana-5883 31 2 observation observation NOUN cana-5883 31 3 is be AUX cana-5883 31 4 understood understand VERB cana-5883 31 5 to to PART cana-5883 31 6 mean mean VERB cana-5883 31 7 that that SCONJ cana-5883 31 8 the the DET cana-5883 31 9 universe universe NOUN cana-5883 31 10 's 's PART cana-5883 31 11 initial initial ADJ cana-5883 31 12 anisotropy anisotropy NOUN cana-5883 31 13 is be AUX cana-5883 31 14 currently currently ADV cana-5883 31 15 changing change VERB cana-5883 31 16 to to ADP cana-5883 31 17 an an DET cana-5883 31 18 isotropy isotropy NOUN cana-5883 31 19 [ [ X cana-5883 31 20 24 24 NUM cana-5883 31 21 - - SYM cana-5883 31 22 25 25 NUM cana-5883 31 23 ] ] PUNCT cana-5883 31 24 . . PUNCT cana-5883 32 1 therefore therefore ADV cana-5883 32 2 , , PUNCT cana-5883 32 3 the the DET cana-5883 32 4 homogeneous homogeneous ADJ cana-5883 32 5 and and CCONJ cana-5883 32 6 anisotropic anisotropic NOUN cana-5883 32 7 bianchi bianchi NOUN cana-5883 32 8 type type NOUN cana-5883 32 9 models model NOUN cana-5883 32 10 can can AUX cana-5883 32 11 be be AUX cana-5883 32 12 quite quite ADV cana-5883 32 13 useful useful ADJ cana-5883 32 14 in in ADP cana-5883 32 15 examining examine VERB cana-5883 32 16 the the DET cana-5883 32 17 universe universe NOUN cana-5883 32 18 's 's PART cana-5883 32 19 early early ADJ cana-5883 32 20 time time NOUN cana-5883 32 21 anisotropic anisotropic NOUN cana-5883 32 22 behaviour behaviour NOUN cana-5883 32 23 . . PUNCT cana-5883 33 1 in in ADP cana-5883 33 2 this this DET cana-5883 33 3 context context NOUN cana-5883 33 4 , , PUNCT cana-5883 33 5 several several ADJ cana-5883 33 6 theories theory NOUN cana-5883 33 7 of of ADP cana-5883 33 8 modified modify VERB cana-5883 33 9 gravity gravity NOUN cana-5883 33 10 were be AUX cana-5883 33 11 later later ADV cana-5883 33 12 developed develop VERB cana-5883 33 13 . . PUNCT cana-5883 34 1 otherwise otherwise ADV cana-5883 34 2 , , PUNCT cana-5883 34 3 f f PROPN cana-5883 34 4 ( ( PUNCT cana-5883 34 5 r r PROPN cana-5883 34 6 , , PUNCT cana-5883 34 7 t t NOUN cana-5883 34 8 ) ) PUNCT cana-5883 34 9 theory theory NOUN cana-5883 34 10 is be AUX cana-5883 34 11 a a DET cana-5883 34 12 further further ADJ cana-5883 34 13 imprecise imprecise ADV cana-5883 34 14 one one NUM cana-5883 34 15 than than ADP cana-5883 34 16 the the DET cana-5883 34 17 f f X cana-5883 34 18 ( ( PUNCT cana-5883 34 19 r r NOUN cana-5883 34 20 ) ) PUNCT cana-5883 34 21 . . PUNCT cana-5883 35 1 geometry geometry NOUN cana-5883 35 2 and and CCONJ cana-5883 35 3 matter matter NOUN cana-5883 35 4 are be AUX cana-5883 35 5 integrated integrate VERB cana-5883 35 6 in in ADP cana-5883 35 7 the the DET cana-5883 35 8 gravitational gravitational ADJ cana-5883 35 9 action action NOUN cana-5883 35 10 to to PART cana-5883 35 11 enlarge enlarge VERB cana-5883 35 12 f f PROPN cana-5883 35 13 ( ( PUNCT cana-5883 35 14 𝑅 𝑅 PROPN cana-5883 35 15 , , PUNCT cana-5883 35 16 𝑇 𝑇 PROPN cana-5883 35 17 ) ) PUNCT cana-5883 35 18 theory theory NOUN cana-5883 35 19 [ [ X cana-5883 35 20 26 26 NUM cana-5883 35 21 ] ] PUNCT cana-5883 35 22 . . PUNCT cana-5883 36 1 gravitational gravitational ADJ cana-5883 36 2 lagrangian lagrangian NOUN cana-5883 36 3 in in ADP cana-5883 36 4 this this DET cana-5883 36 5 alter alter NOUN cana-5883 36 6 gravity gravity NOUN cana-5883 36 7 theory theory NOUN cana-5883 36 8 requires require VERB cana-5883 36 9 an an DET cana-5883 36 10 unknown unknown ADJ cana-5883 36 11 function function NOUN cana-5883 36 12 of of ADP cana-5883 36 13 the the DET cana-5883 36 14 scalar scalar ADJ cana-5883 36 15 curvature curvature NOUN cana-5883 36 16 and and CCONJ cana-5883 36 17 the the DET cana-5883 36 18 stress stress ADJ cana-5883 36 19 energy energy NOUN cana-5883 36 20 - - PUNCT cana-5883 36 21 momentum momentum NOUN cana-5883 36 22 tensor tensor NOUN cana-5883 36 23 trace trace NOUN cana-5883 36 24 . . PUNCT cana-5883 37 1 astronomers astronomer NOUN cana-5883 37 2 who who PRON cana-5883 37 3 have have AUX cana-5883 37 4 researched research VERB cana-5883 37 5 contemporary contemporary ADJ cana-5883 37 6 cosmological cosmological ADJ cana-5883 37 7 issues issue NOUN cana-5883 37 8 like like VERB cana-5883 37 9 as as ADP cana-5883 37 10 dark dark ADJ cana-5883 37 11 energy energy NOUN cana-5883 37 12 and and CCONJ cana-5883 37 13 anisotropy anisotropy NOUN cana-5883 37 14 have have VERB cana-5883 37 15 a a DET cana-5883 37 16 tendency tendency NOUN cana-5883 37 17 to to PART cana-5883 37 18 look look VERB cana-5883 37 19 at at ADP cana-5883 37 20 modified modified ADJ cana-5883 37 21 theories theory NOUN cana-5883 37 22 involving involve VERB cana-5883 37 23 bianchi bianchi NOUN cana-5883 37 24 type type NOUN cana-5883 37 25 models model NOUN cana-5883 37 26 . . PUNCT cana-5883 38 1 formerly formerly ADV cana-5883 38 2 ten ten NUM cana-5883 38 3 years year NOUN cana-5883 38 4 f f PROPN cana-5883 38 5 ( ( PUNCT cana-5883 38 6 r r NOUN cana-5883 38 7 , , PUNCT cana-5883 38 8 t t NOUN cana-5883 38 9 ) ) PUNCT cana-5883 38 10 gravity gravity NOUN cana-5883 38 11 assumption assumption NOUN cana-5883 38 12 increased increase VERB cana-5883 38 13 attention attention NOUN cana-5883 38 14 , , PUNCT cana-5883 38 15 among among ADP cana-5883 38 16 other other ADJ cana-5883 38 17 things thing NOUN cana-5883 38 18 . . PUNCT cana-5883 39 1 in in ADP cana-5883 39 2 this this DET cana-5883 39 3 context context NOUN cana-5883 39 4 , , PUNCT cana-5883 39 5 a a DET cana-5883 39 6 large large ADJ cana-5883 39 7 number number NOUN cana-5883 39 8 of of ADP cana-5883 39 9 studies study NOUN cana-5883 39 10 exist exist VERB cana-5883 39 11 . . PUNCT cana-5883 40 1 in in ADP cana-5883 40 2 f f PROPN cana-5883 40 3 ( ( PUNCT cana-5883 40 4 r r PROPN cana-5883 40 5 , , PUNCT cana-5883 40 6 t t NOUN cana-5883 40 7 ) ) PUNCT cana-5883 40 8 gravity gravity NOUN cana-5883 40 9 , , PUNCT cana-5883 40 10 adhav adhav PROPN cana-5883 40 11 stumbled stumble VERB cana-5883 40 12 on on ADP cana-5883 40 13 errorless errorless ADJ cana-5883 40 14 solutions solution NOUN cana-5883 40 15 to to ADP cana-5883 40 16 the the DET cana-5883 40 17 field field NOUN cana-5883 40 18 equations equation NOUN cana-5883 40 19 with with ADP cana-5883 40 20 view view NOUN cana-5883 40 21 to to ADP cana-5883 40 22 lrs lrs PROPN cana-5883 40 23 bianchi bianchi PROPN cana-5883 40 24 type type PROPN cana-5883 40 25 - - PUNCT cana-5883 40 26 i i PRON cana-5883 40 27 space space NOUN cana-5883 40 28 [ [ X cana-5883 40 29 27 27 NUM cana-5883 40 30 ] ] PUNCT cana-5883 40 31 . . PUNCT cana-5883 41 1 by by ADP cana-5883 41 2 embracing embrace VERB cana-5883 41 3 a a DET cana-5883 41 4 linearly linearly ADV cana-5883 41 5 substituting substitute VERB cana-5883 41 6 deceleration deceleration NOUN cana-5883 41 7 parameter parameter NOUN cana-5883 41 8 and and CCONJ cana-5883 41 9 taking take VERB cana-5883 41 10 into into ADP cana-5883 41 11 account account NOUN cana-5883 41 12 numerous numerous ADJ cana-5883 41 13 functional functional ADJ cana-5883 41 14 configurations configuration NOUN cana-5883 41 15 of of ADP cana-5883 41 16 𝑓 𝑓 DET cana-5883 41 17 ( ( PUNCT cana-5883 41 18 𝑅 𝑅 PROPN cana-5883 41 19 , , PUNCT cana-5883 41 20 𝑇 𝑇 PROPN cana-5883 41 21 ) ) PUNCT cana-5883 41 22 sahoo sahoo PROPN cana-5883 41 23 and and CCONJ cana-5883 41 24 sivakumar sivakumar PROPN cana-5883 41 25 obtained obtain VERB cana-5883 41 26 the the DET cana-5883 41 27 require require NOUN cana-5883 41 28 solutions solution NOUN cana-5883 41 29 for for ADP cana-5883 41 30 lrs lrs PROPN cana-5883 41 31 bianchi bianchi PROPN cana-5883 41 32 type type PROPN cana-5883 41 33 - - PUNCT cana-5883 41 34 i i PRON cana-5883 41 35 cosmological cosmological ADJ cana-5883 41 36 models model NOUN cana-5883 41 37 in in ADP cana-5883 41 38 𝑓 𝑓 DET cana-5883 41 39 ( ( PUNCT cana-5883 41 40 𝑅 𝑅 PROPN cana-5883 41 41 , , PUNCT cana-5883 41 42 𝑇 𝑇 PROPN cana-5883 41 43 ) ) PUNCT cana-5883 41 44 theory theory NOUN cana-5883 41 45 of of ADP cana-5883 41 46 gravity gravity NOUN cana-5883 41 47 [ [ X cana-5883 41 48 28 28 NUM cana-5883 41 49 ] ] PUNCT cana-5883 41 50 . . PUNCT cana-5883 42 1 the the DET cana-5883 42 2 wordsmith wordsmith NOUN cana-5883 42 3 concluded conclude VERB cana-5883 42 4 that that SCONJ cana-5883 42 5 there there PRON cana-5883 42 6 is be VERB cana-5883 42 7 no no DET cana-5883 42 8 way way NOUN cana-5883 42 9 to to PART cana-5883 42 10 avoid avoid VERB cana-5883 42 11 the the DET cana-5883 42 12 big big ADJ cana-5883 42 13 rip rip NOUN cana-5883 42 14 scenario scenario NOUN cana-5883 42 15 . . PUNCT cana-5883 43 1 using use VERB cana-5883 43 2 the the DET cana-5883 43 3 presumption presumption NOUN cana-5883 43 4 of of ADP cana-5883 43 5 the the DET cana-5883 43 6 constant constant ADJ cana-5883 43 7 deceleration deceleration NOUN cana-5883 43 8 parameter parameter NOUN cana-5883 43 9 for for ADP cana-5883 43 10 bianchi bianchi NOUN cana-5883 43 11 type type NOUN cana-5883 43 12 - - PUNCT cana-5883 43 13 v v NOUN cana-5883 43 14 space space NOUN cana-5883 43 15 - - PUNCT cana-5883 43 16 time time NOUN cana-5883 43 17 in in ADP cana-5883 43 18 the the DET cana-5883 43 19 f(r f(r PROPN cana-5883 43 20 , , PUNCT cana-5883 43 21 t t NOUN cana-5883 43 22 ) ) PUNCT cana-5883 43 23 theory theory NOUN cana-5883 43 24 of of ADP cana-5883 43 25 gravity gravity NOUN cana-5883 43 26 and and CCONJ cana-5883 43 27 the the DET cana-5883 43 28 variant variant ADJ cana-5883 43 29 law law NOUN cana-5883 43 30 of of ADP cana-5883 43 31 the the DET cana-5883 43 32 hubble hubble ADJ cana-5883 43 33 parameter parameter NOUN cana-5883 43 34 , , PUNCT cana-5883 43 35 shamir shamir PROPN cana-5883 43 36 set set VERB cana-5883 43 37 up up ADP cana-5883 43 38 two two NUM cana-5883 43 39 exact exact ADJ cana-5883 43 40 solutions solution NOUN cana-5883 43 41 that that PRON cana-5883 43 42 correlate correlate VERB cana-5883 43 43 with with ADP cana-5883 43 44 singular singular ADJ cana-5883 43 45 and and CCONJ cana-5883 43 46 non non ADJ cana-5883 43 47 - - ADJ cana-5883 43 48 singular singular ADJ cana-5883 43 49 models model NOUN cana-5883 44 1 [ [ X cana-5883 44 2 29].using 29].use VERB cana-5883 44 3 a a DET cana-5883 44 4 linear linear ADJ cana-5883 44 5 deceleration deceleration NOUN cana-5883 44 6 parameter parameter NOUN cana-5883 44 7 with with ADP cana-5883 44 8 a a DET cana-5883 44 9 negative negative ADJ cana-5883 44 10 slope slope NOUN cana-5883 44 11 , , PUNCT cana-5883 44 12 chaubey chaubey VERB cana-5883 44 13 et et PROPN cana-5883 44 14 al al PROPN cana-5883 44 15 . . PROPN cana-5883 44 16 analysed analyse VERB cana-5883 44 17 the the DET cana-5883 44 18 broad broad ADJ cana-5883 44 19 class class NOUN cana-5883 44 20 of of ADP cana-5883 44 21 bianchi bianchi NOUN cana-5883 44 22 cosmological cosmological ADJ cana-5883 44 23 models model NOUN cana-5883 44 24 in in ADP cana-5883 44 25 f(𝑅 f(𝑅 PROPN cana-5883 44 26 , , PUNCT cana-5883 44 27 𝑇 𝑇 PROPN cana-5883 44 28 ) ) PUNCT cana-5883 44 29 gravity gravity NOUN cana-5883 44 30 with with ADP cana-5883 44 31 dark dark ADJ cana-5883 44 32 energy energy NOUN cana-5883 44 33 as as ADP cana-5883 44 34 standard standard ADJ cana-5883 44 35 and and CCONJ cana-5883 44 36 modified modify VERB cana-5883 44 37 chaplygin chaplygin NOUN cana-5883 44 38 gas gas NOUN cana-5883 44 39 and and CCONJ cana-5883 44 40 bulk bulk ADJ cana-5883 44 41 viscosity viscosity NOUN cana-5883 44 42 for for ADP cana-5883 44 43 three three NUM cana-5883 44 44 types type NOUN cana-5883 44 45 of of ADP cana-5883 44 46 average average ADJ cana-5883 44 47 scale scale NOUN cana-5883 44 48 factor factor NOUN cana-5883 44 49 [ [ X cana-5883 44 50 30 30 NUM cana-5883 44 51 ] ] PUNCT cana-5883 44 52 . . PUNCT cana-5883 45 1 flrw flrw PROPN cana-5883 45 2 cosmological cosmological ADJ cana-5883 45 3 model model NOUN cana-5883 45 4 with with ADP cana-5883 45 5 orthogonal orthogonal ADJ cana-5883 45 6 deceleration deceleration NOUN cana-5883 45 7 parameter parameter NOUN cana-5883 45 8 in in ADP cana-5883 45 9 f f PROPN cana-5883 45 10 ( ( PUNCT cana-5883 45 11 r r PROPN cana-5883 45 12 , , PUNCT cana-5883 45 13 t t NOUN cana-5883 45 14 ) ) PUNCT cana-5883 45 15 gravity gravity NOUN cana-5883 45 16 has have AUX cana-5883 45 17 been be AUX cana-5883 45 18 scrutinize scrutinize VERB cana-5883 45 19 by by ADP cana-5883 45 20 bishi bishi PROPN cana-5883 45 21 et et PROPN cana-5883 45 22 al al PROPN cana-5883 45 23 . . PUNCT cana-5883 46 1 [ [ X cana-5883 46 2 31 31 NUM cana-5883 46 3 ] ] PUNCT cana-5883 46 4 . . PUNCT cana-5883 47 1 moreover moreover ADV cana-5883 47 2 , , PUNCT cana-5883 47 3 using use VERB cana-5883 47 4 a a DET cana-5883 47 5 unique unique ADJ cana-5883 47 6 form form NOUN cana-5883 47 7 of of ADP cana-5883 47 8 hubble hubble NOUN cana-5883 47 9 's 's PART cana-5883 47 10 parameter parameter NOUN cana-5883 47 11 , , PUNCT cana-5883 47 12 bishi bishi PROPN cana-5883 47 13 , , PUNCT cana-5883 47 14 et et PROPN cana-5883 47 15 al al PROPN cana-5883 47 16 . . PROPN cana-5883 47 17 range range PROPN cana-5883 47 18 over over ADP cana-5883 47 19 the the DET cana-5883 47 20 lrs lrs PROPN cana-5883 47 21 bianchi bianchi PROPN cana-5883 47 22 type type PROPN cana-5883 47 23 - - PUNCT cana-5883 47 24 i i PRON cana-5883 47 25 cosmological cosmological ADJ cana-5883 47 26 model model NOUN cana-5883 47 27 in in ADP cana-5883 47 28 f f PROPN cana-5883 47 29 ( ( PUNCT cana-5883 47 30 r r PROPN cana-5883 47 31 , , PUNCT cana-5883 47 32 t t NOUN cana-5883 47 33 ) ) PUNCT cana-5883 47 34 gravity gravity NOUN cana-5883 48 1 [ [ X cana-5883 48 2 32 32 NUM cana-5883 48 3 ] ] PUNCT cana-5883 48 4 . . PUNCT cana-5883 49 1 for for ADP cana-5883 49 2 lrs lrs PROPN cana-5883 49 3 bianchi bianchi PROPN cana-5883 49 4 type type PROPN cana-5883 49 5 - - PUNCT cana-5883 49 6 i i PRON cana-5883 49 7 model model NOUN cana-5883 49 8 , , PUNCT cana-5883 49 9 tiwari tiwari PROPN cana-5883 49 10 et et PROPN cana-5883 49 11 al al PROPN cana-5883 49 12 . . PROPN cana-5883 49 13 derived derive VERB cana-5883 49 14 the the DET cana-5883 49 15 suspension suspension NOUN cana-5883 49 16 to to ADP cana-5883 49 17 the the DET cana-5883 49 18 field field NOUN cana-5883 49 19 equations equation NOUN cana-5883 49 20 of of ADP cana-5883 49 21 f f PROPN cana-5883 49 22 ( ( PUNCT cana-5883 49 23 𝑅 𝑅 PROPN cana-5883 49 24 , , PUNCT cana-5883 49 25 𝑇 𝑇 PROPN cana-5883 49 26 ) ) PUNCT cana-5883 49 27 gravity gravity NOUN cana-5883 49 28 by by ADP cana-5883 49 29 assuming assume VERB cana-5883 49 30 that that SCONJ cana-5883 49 31 the the DET cana-5883 49 32 deceleration deceleration NOUN cana-5883 49 33 parameter parameter NOUN cana-5883 49 34 is be AUX cana-5883 49 35 a a DET cana-5883 49 36 linear linear ADJ cana-5883 49 37 function function NOUN cana-5883 49 38 of of ADP cana-5883 49 39 the the DET cana-5883 49 40 hubble hubble ADJ cana-5883 49 41 parameter parameter NOUN cana-5883 49 42 and and CCONJ cana-5883 49 43 indicated indicate VERB cana-5883 49 44 that that SCONJ cana-5883 49 45 the the DET cana-5883 49 46 model model NOUN cana-5883 49 47 starts start VERB cana-5883 49 48 with with ADP cana-5883 49 49 an an DET cana-5883 49 50 initial initial ADJ cana-5883 49 51 singular singular ADJ cana-5883 49 52 phase phase NOUN cana-5883 49 53 and and CCONJ cana-5883 49 54 transitions transition NOUN cana-5883 49 55 from from ADP cana-5883 49 56 an an DET cana-5883 49 57 early early ADJ cana-5883 49 58 deceleration deceleration NOUN cana-5883 49 59 phase phase NOUN cana-5883 49 60 to to ADP cana-5883 49 61 a a DET cana-5883 49 62 late late ADJ cana-5883 49 63 - - PUNCT cana-5883 49 64 time time NOUN cana-5883 49 65 acceleration acceleration NOUN cana-5883 49 66 phase phase NOUN cana-5883 49 67 [ [ X cana-5883 49 68 33 33 NUM cana-5883 49 69 ] ] PUNCT cana-5883 49 70 . . PUNCT cana-5883 50 1 mamon mamon PROPN cana-5883 50 2 and and CCONJ cana-5883 50 3 das das PROPN cana-5883 50 4 have have AUX cana-5883 50 5 examined examine VERB cana-5883 50 6 the the DET cana-5883 50 7 field field NOUN cana-5883 50 8 equations equation NOUN cana-5883 50 9 of of ADP cana-5883 50 10 f f PROPN cana-5883 50 11 ( ( PUNCT cana-5883 50 12 𝑅 𝑅 PROPN cana-5883 50 13 , , PUNCT cana-5883 50 14 𝑇 𝑇 PROPN cana-5883 50 15 ) ) PUNCT cana-5883 50 16 gravity gravity NOUN cana-5883 50 17 for for ADP cana-5883 50 18 the the DET cana-5883 50 19 parametric parametric ADJ cana-5883 50 20 remodelling remodelling NOUN cana-5883 50 21 model model NOUN cana-5883 50 22 of of ADP cana-5883 50 23 the the DET cana-5883 50 24 deceleration deceleration NOUN cana-5883 50 25 parameter parameter NOUN cana-5883 51 1 [ [ X cana-5883 51 2 34 34 NUM cana-5883 51 3 ] ] PUNCT cana-5883 51 4 . . PUNCT cana-5883 52 1 existed exist VERB cana-5883 52 2 come come VERB cana-5883 52 3 across across ADP cana-5883 52 4 that that SCONJ cana-5883 52 5 the the DET cana-5883 52 6 obtained obtain VERB cana-5883 52 7 model model NOUN cana-5883 52 8 of of ADP cana-5883 52 9 the the DET cana-5883 52 10 universe universe NOUN cana-5883 52 11 restrain restrain VERB cana-5883 52 12 an an DET cana-5883 52 13 initial initial ADJ cana-5883 52 14 singularity singularity NOUN cana-5883 52 15 , , PUNCT cana-5883 52 16 a a DET cana-5883 52 17 finite finite ADJ cana-5883 52 18 life life NOUN cana-5883 52 19 full full ADJ cana-5883 52 20 lenght lenght ADJ cana-5883 52 21 , , PUNCT cana-5883 52 22 and and CCONJ cana-5883 52 23 a a DET cana-5883 52 24 big big ADJ cana-5883 52 25 rip rip NOUN cana-5883 52 26 at at ADP cana-5883 52 27 the the DET cana-5883 52 28 end end NOUN cana-5883 52 29 . . PUNCT cana-5883 53 1 akarsu akarsu NOUN cana-5883 53 2 and and CCONJ cana-5883 53 3 dereli dereli PROPN cana-5883 53 4 explored explore VERB cana-5883 53 5 cosmological cosmological ADJ cana-5883 53 6 models model NOUN cana-5883 53 7 in in ADP cana-5883 53 8 which which PRON cana-5883 53 9 the the DET cana-5883 53 10 cosmos cosmos PROPN cana-5883 53 11 evinces evince VERB cana-5883 53 12 quintom quintom NOUN cana-5883 53 13 like like ADP cana-5883 53 14 behavior behavior NOUN cana-5883 53 15 and and CCONJ cana-5883 53 16 bring bring VERB cana-5883 53 17 to to ADP cana-5883 53 18 a a DET cana-5883 53 19 conclusion conclusion NOUN cana-5883 53 20 in in ADP cana-5883 53 21 a a DET cana-5883 53 22 large large ADJ cana-5883 53 23 rip rip NOUN cana-5883 53 24 with with ADP cana-5883 53 25 a a DET cana-5883 53 26 linearly linearly ADV cana-5883 53 27 diverse diverse ADJ cana-5883 53 28 deceleration deceleration NOUN cana-5883 53 29 value value NOUN cana-5883 53 30 [ [ X cana-5883 53 31 35 35 NUM cana-5883 53 32 ] ] PUNCT cana-5883 53 33 . . PUNCT cana-5883 54 1 the the DET cana-5883 54 2 big big ADJ cana-5883 54 3 - - PUNCT cana-5883 54 4 rip rip NOUN cana-5883 54 5 theory theory NOUN cana-5883 54 6 advance advance NOUN cana-5883 54 7 that that SCONJ cana-5883 54 8 the the DET cana-5883 54 9 universe universe NOUN cana-5883 54 10 expands expand VERB cana-5883 54 11 before before SCONJ cana-5883 54 12 communications communication NOUN cana-5883 54 13 on on ADP cana-5883 54 14 applied apply VERB cana-5883 54 15 nonlinear nonlinear ADJ cana-5883 54 16 analysis analysis NOUN cana-5883 54 17 issn issn NOUN cana-5883 54 18 : : PUNCT cana-5883 54 19 1074 1074 NUM cana-5883 54 20 - - PUNCT cana-5883 54 21 133x 133x NUM cana-5883 54 22 vol vol NOUN cana-5883 54 23 32 32 NUM cana-5883 54 24 no no NOUN cana-5883 54 25 . . PUNCT cana-5883 55 1 2s 2s NUM cana-5883 55 2 ( ( PUNCT cana-5883 55 3 2025 2025 NUM cana-5883 55 4 ) ) PUNCT cana-5883 55 5 606 606 NUM cana-5883 55 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 55 7 shrinking shrink VERB cana-5883 55 8 and and CCONJ cana-5883 55 9 moving move VERB cana-5883 55 10 back back ADV cana-5883 55 11 to to ADP cana-5883 55 12 its its PRON cana-5883 55 13 initial initial ADJ cana-5883 55 14 state state NOUN cana-5883 55 15 at at ADP cana-5883 55 16 the the DET cana-5883 55 17 time time NOUN cana-5883 55 18 of of ADP cana-5883 55 19 the the DET cana-5883 55 20 big big PROPN cana-5883 55 21 bang bang PROPN cana-5883 55 22 . . PROPN cana-5883 55 23 bakry bakry PROPN cana-5883 55 24 and and CCONJ cana-5883 55 25 shafeek shafeek PROPN cana-5883 55 26 glanced glance VERB cana-5883 55 27 into into ADP cana-5883 55 28 the the DET cana-5883 55 29 universe universe ADJ cana-5883 55 30 model model NOUN cana-5883 55 31 with with ADP cana-5883 55 32 the the DET cana-5883 55 33 time time NOUN cana-5883 55 34 - - PUNCT cana-5883 55 35 dependent dependent ADJ cana-5883 55 36 deceleration deceleration NOUN cana-5883 55 37 parameter parameter NOUN cana-5883 55 38 of of ADP cana-5883 55 39 the the DET cana-5883 55 40 second second ADJ cana-5883 55 41 degree degree NOUN cana-5883 55 42 and and CCONJ cana-5883 55 43 came come VERB cana-5883 55 44 to to ADP cana-5883 55 45 this this DET cana-5883 55 46 inference inference NOUN cana-5883 55 47 [ [ X cana-5883 55 48 36 36 NUM cana-5883 55 49 ] ] PUNCT cana-5883 55 50 . . PUNCT cana-5883 56 1 tiwari tiwari PROPN cana-5883 56 2 et et PROPN cana-5883 56 3 al al PROPN cana-5883 56 4 . . PUNCT cana-5883 57 1 inquire inquire VERB cana-5883 57 2 into into ADP cana-5883 57 3 the the DET cana-5883 57 4 time time NOUN cana-5883 57 5 - - PUNCT cana-5883 57 6 dependent dependent ADJ cana-5883 57 7 deceleration deceleration NOUN cana-5883 57 8 parameter parameter NOUN cana-5883 57 9 in in ADP cana-5883 57 10 the the DET cana-5883 57 11 framework framework NOUN cana-5883 57 12 of of ADP cana-5883 57 13 f f PROPN cana-5883 57 14 ( ( PUNCT cana-5883 57 15 r r PROPN cana-5883 57 16 , , PUNCT cana-5883 57 17 t t NOUN cana-5883 57 18 ) ) PUNCT cana-5883 57 19 gravity gravity NOUN cana-5883 57 20 and and CCONJ cana-5883 57 21 concluded conclude VERB cana-5883 57 22 that that SCONJ cana-5883 57 23 the the DET cana-5883 57 24 cosmos cosmos PROPN cana-5883 57 25 has have AUX cana-5883 57 26 become become VERB cana-5883 57 27 distended distend VERB cana-5883 57 28 periodically periodically ADV cana-5883 57 29 . . PUNCT cana-5883 58 1 i.e. i.e. X cana-5883 58 2 , , PUNCT cana-5883 58 3 the the DET cana-5883 58 4 universe universe ADJ cana-5883 58 5 expansion expansion NOUN cana-5883 58 6 at at ADP cana-5883 58 7 embarks embark NOUN cana-5883 58 8 on on ADP cana-5883 58 9 with with ADP cana-5883 58 10 a a DET cana-5883 58 11 slowing slow VERB cana-5883 58 12 then then ADV cana-5883 58 13 facilitate facilitate VERB cana-5883 58 14 super super ADV cana-5883 58 15 exponentially exponentially ADV cana-5883 58 16 [ [ X cana-5883 58 17 37 37 NUM cana-5883 58 18 ] ] PUNCT cana-5883 58 19 . . PUNCT cana-5883 59 1 according accord VERB cana-5883 59 2 to to ADP cana-5883 59 3 tiwari tiwari NOUN cana-5883 59 4 and and CCONJ cana-5883 59 5 sofuoglu sofuoglu NOUN cana-5883 59 6 's 's PART cana-5883 59 7 compulsion compulsion NOUN cana-5883 59 8 investigation investigation NOUN cana-5883 59 9 of of ADP cana-5883 59 10 quadratic quadratic ADJ cana-5883 59 11 changing change VERB cana-5883 59 12 deceleration deceleration NOUN cana-5883 59 13 parameter parameter NOUN cana-5883 59 14 in in ADP cana-5883 59 15 the the DET cana-5883 59 16 context context NOUN cana-5883 59 17 of of ADP cana-5883 59 18 f f PROPN cana-5883 59 19 ( ( PUNCT cana-5883 59 20 r r PROPN cana-5883 59 21 , , PUNCT cana-5883 59 22 t t NOUN cana-5883 59 23 ) ) PUNCT cana-5883 59 24 gravity gravity NOUN cana-5883 59 25 , , PUNCT cana-5883 59 26 universe universe NOUN cana-5883 59 27 set set VERB cana-5883 59 28 about about ADP cana-5883 59 29 with with ADP cana-5883 59 30 a a DET cana-5883 59 31 big big ADJ cana-5883 59 32 bang bang NOUN cana-5883 59 33 and and CCONJ cana-5883 59 34 ends end VERB cana-5883 59 35 with with ADP cana-5883 59 36 a a DET cana-5883 59 37 enormous enormous ADJ cana-5883 59 38 rip rip NOUN cana-5883 59 39 [ [ X cana-5883 59 40 38 38 NUM cana-5883 59 41 ] ] PUNCT cana-5883 59 42 . . PUNCT cana-5883 60 1 kumar kumar PROPN cana-5883 60 2 and and CCONJ cana-5883 60 3 arora arora PROPN cana-5883 60 4 have have AUX cana-5883 60 5 studied study VERB cana-5883 60 6 bi bi ADJ cana-5883 60 7 - - ADJ cana-5883 60 8 quadratic quadratic ADJ cana-5883 60 9 varying vary VERB cana-5883 60 10 deceleration deceleration NOUN cana-5883 60 11 parameter parameter NOUN cana-5883 60 12 to to PART cana-5883 60 13 study study VERB cana-5883 60 14 the the DET cana-5883 60 15 cosmological cosmological ADJ cana-5883 60 16 model model NOUN cana-5883 60 17 [ [ X cana-5883 60 18 39 39 NUM cana-5883 60 19 ] ] PUNCT cana-5883 60 20 . . PUNCT cana-5883 61 1 mishra mishra PROPN cana-5883 61 2 et et PROPN cana-5883 61 3 al al PROPN cana-5883 61 4 . . PROPN cana-5883 61 5 have have AUX cana-5883 61 6 provided provide VERB cana-5883 61 7 a a DET cana-5883 61 8 comprehensive comprehensive ADJ cana-5883 61 9 analysis analysis NOUN cana-5883 61 10 of of ADP cana-5883 61 11 the the DET cana-5883 61 12 evolution evolution NOUN cana-5883 61 13 of of ADP cana-5883 61 14 geometrical geometrical ADJ cana-5883 61 15 and and CCONJ cana-5883 61 16 physical physical ADJ cana-5883 61 17 parameters parameter NOUN cana-5883 61 18 , , PUNCT cana-5883 61 19 complete complete ADJ cana-5883 61 20 with with ADP cana-5883 61 21 the the DET cana-5883 61 22 numerically numerically ADV cana-5883 61 23 constrained constrain VERB cana-5883 61 24 values.[40 values.[40 NOUN cana-5883 61 25 ] ] PUNCT cana-5883 61 26 . . PUNCT cana-5883 62 1 in in ADP cana-5883 62 2 this this DET cana-5883 62 3 paper paper NOUN cana-5883 62 4 , , PUNCT cana-5883 62 5 we we PRON cana-5883 62 6 have have AUX cana-5883 62 7 evolved evolve VERB cana-5883 62 8 anisotropic anisotropic NOUN cana-5883 62 9 cosmological cosmological ADJ cana-5883 62 10 model model NOUN cana-5883 62 11 in in ADP cana-5883 62 12 f(𝑅 f(𝑅 PROPN cana-5883 62 13 , , PUNCT cana-5883 62 14 𝑇 𝑇 PROPN cana-5883 62 15 ) ) PUNCT cana-5883 62 16 gravity gravity NOUN cana-5883 62 17 theory theory NOUN cana-5883 62 18 to to PART cana-5883 62 19 acquire acquire VERB cana-5883 62 20 the the DET cana-5883 62 21 exact exact ADJ cana-5883 62 22 solution solution NOUN cana-5883 62 23 of of ADP cana-5883 62 24 the the DET cana-5883 62 25 alter alter PROPN cana-5883 62 26 field field NOUN cana-5883 62 27 equations equation NOUN cana-5883 62 28 in in ADP cana-5883 62 29 the the DET cana-5883 62 30 activity activity NOUN cana-5883 62 31 of of ADP cana-5883 62 32 the the DET cana-5883 62 33 newly newly ADV cana-5883 62 34 offered offer VERB cana-5883 62 35 condition condition NOUN cana-5883 62 36 of of ADP cana-5883 62 37 [ [ X cana-5883 62 38 36 36 NUM cana-5883 62 39 ] ] PUNCT cana-5883 62 40 quadratic quadratic ADJ cana-5883 62 41 form form NOUN cana-5883 62 42 of of ADP cana-5883 62 43 deceleration deceleration NOUN cana-5883 62 44 parameter parameter NOUN cana-5883 62 45 and and CCONJ cana-5883 62 46 requiring require VERB cana-5883 62 47 the the DET cana-5883 62 48 functional functional ADJ cana-5883 62 49 form form NOUN cana-5883 62 50 of of ADP cana-5883 62 51 f(𝑅 f(𝑅 NUM cana-5883 62 52 , , PUNCT cana-5883 62 53 𝑇 𝑇 PROPN cana-5883 62 54 ) ) PUNCT cana-5883 62 55 = = SYM cana-5883 63 1 f1(r f1(r PROPN cana-5883 63 2 ) ) PUNCT cana-5883 63 3 + + NUM cana-5883 63 4 f2(t f2(t PROPN cana-5883 63 5 ) ) PUNCT cana-5883 63 6 , , PUNCT cana-5883 63 7 where where SCONJ cana-5883 63 8 f1(r f1(r NOUN cana-5883 63 9 ) ) PUNCT cana-5883 63 10 = = SYM cana-5883 63 11 πœ† πœ† PROPN cana-5883 63 12 𝑅 𝑅 PROPN cana-5883 63 13 and and CCONJ cana-5883 63 14 f2(t f2(t PROPN cana-5883 63 15 ) ) PUNCT cana-5883 63 16 = = SYM cana-5883 63 17 πœ† πœ† DET cana-5883 63 18 𝑇. 𝑇. PROPN cana-5883 63 19 the the DET cana-5883 63 20 tangible tangible ADJ cana-5883 63 21 major major NOUN cana-5883 63 22 of of ADP cana-5883 63 23 the the DET cana-5883 63 24 considered consider VERB cana-5883 63 25 deceleration deceleration NOUN cana-5883 63 26 parameter parameter NOUN cana-5883 63 27 is be AUX cana-5883 63 28 presented present VERB cana-5883 63 29 as as ADP cana-5883 63 30 ; ; PUNCT cana-5883 63 31 the the DET cana-5883 63 32 cosmological cosmological ADJ cana-5883 63 33 model model NOUN cana-5883 63 34 starts start VERB cana-5883 63 35 with with ADP cana-5883 63 36 a a DET cana-5883 63 37 big big ADJ cana-5883 63 38 bang bang NOUN cana-5883 63 39 at at ADP cana-5883 63 40 t t PROPN cana-5883 63 41 = = SYM cana-5883 63 42 0 0 PUNCT cana-5883 63 43 and and CCONJ cana-5883 63 44 ends end VERB cana-5883 63 45 at at ADP cana-5883 63 46 a a DET cana-5883 63 47 big big ADJ cana-5883 63 48 rip rip NOUN cana-5883 63 49 at at ADP cana-5883 63 50 t=2𝛽 t=2𝛽 NOUN cana-5883 63 51 i.e. i.e. ADV cana-5883 63 52 , , PUNCT cana-5883 63 53 the the DET cana-5883 63 54 universe universe NOUN cana-5883 63 55 β€˜ ' PUNCT cana-5883 63 56 begins begin VERB cana-5883 63 57 ’ ' PUNCT cana-5883 63 58 with with ADP cana-5883 63 59 q q PROPN cana-5883 63 60 = = SYM cana-5883 63 61 ( ( PUNCT cana-5883 63 62 8 8 NUM cana-5883 63 63 𝛽2 𝛽2 NOUN cana-5883 63 64 βˆ’ βˆ’ PROPN cana-5883 63 65 1 1 NUM cana-5883 63 66 ) ) PUNCT cana-5883 63 67 and and CCONJ cana-5883 63 68 ends end VERB cana-5883 63 69 with with ADP cana-5883 63 70 q q PROPN cana-5883 63 71 = = SYM cana-5883 63 72 ( ( PUNCT cana-5883 63 73 -4 -4 INTJ cana-5883 63 74 𝛽2 𝛽2 PROPN cana-5883 63 75 βˆ’ βˆ’ PROPN cana-5883 63 76 1 1 NUM cana-5883 63 77 ) ) PUNCT cana-5883 63 78 . . PUNCT cana-5883 64 1 ii ii PROPN cana-5883 64 2 . . PUNCT cana-5883 64 3 basic basic ADJ cana-5883 64 4 formalism formalism NOUN cana-5883 64 5 of of ADP cana-5883 64 6 f f PROPN cana-5883 64 7 ( ( PUNCT cana-5883 64 8 r r PROPN cana-5883 64 9 , , PUNCT cana-5883 64 10 t t NOUN cana-5883 64 11 ) ) PUNCT cana-5883 64 12 gravity gravity NOUN cana-5883 64 13 theory theory NOUN cana-5883 64 14 : : PUNCT cana-5883 64 15 in in ADP cana-5883 64 16 f f PROPN cana-5883 64 17 ( ( PUNCT cana-5883 64 18 r r PROPN cana-5883 64 19 , , PUNCT cana-5883 64 20 t t NOUN cana-5883 64 21 ) ) PUNCT cana-5883 64 22 gravity gravity NOUN cana-5883 64 23 , , PUNCT cana-5883 64 24 the the DET cana-5883 64 25 field field NOUN cana-5883 64 26 equations equation NOUN cana-5883 64 27 are be AUX cana-5883 64 28 obtained obtain VERB cana-5883 64 29 from from ADP cana-5883 64 30 a a DET cana-5883 64 31 dissimilarity dissimilarity NOUN cana-5883 64 32 , , PUNCT cana-5883 64 33 hilbert hilbert NOUN cana-5883 64 34 - - PUNCT cana-5883 64 35 einstein einstein PROPN cana-5883 64 36 type type NOUN cana-5883 64 37 , , PUNCT cana-5883 64 38 principle principle NOUN cana-5883 64 39 . . PUNCT cana-5883 65 1 the the DET cana-5883 65 2 action action NOUN cana-5883 65 3 for for ADP cana-5883 65 4 the the DET cana-5883 65 5 specified specified ADJ cana-5883 65 6 f f NOUN cana-5883 65 7 ( ( PUNCT cana-5883 65 8 r r NOUN cana-5883 65 9 , , PUNCT cana-5883 65 10 t t NOUN cana-5883 65 11 ) ) PUNCT cana-5883 65 12 gravity gravity NOUN cana-5883 65 13 is be AUX cana-5883 65 14 , , PUNCT cana-5883 65 15 s s PART cana-5883 65 16 = = X cana-5883 65 17 ∫ ∫ PROPN cana-5883 65 18 ( ( PUNCT cana-5883 65 19 1 1 NUM cana-5883 65 20 16Ο€ 16Ο€ NOUN cana-5883 65 21 f(r f(r PROPN cana-5883 65 22 , , PUNCT cana-5883 65 23 t t PROPN cana-5883 65 24 ) ) PUNCT cana-5883 65 25 + + CCONJ cana-5883 65 26 sm)βˆšβˆ’π‘” sm)βˆšβˆ’π‘” NUM cana-5883 65 27 𝑑π‘₯4 𝑑π‘₯4 PROPN cana-5883 65 28 ( ( PUNCT cana-5883 65 29 1 1 NUM cana-5883 65 30 ) ) PUNCT cana-5883 65 31 where where SCONJ cana-5883 65 32 f f PROPN cana-5883 65 33 ( ( PUNCT cana-5883 65 34 r r PROPN cana-5883 65 35 , , PUNCT cana-5883 65 36 t t PROPN cana-5883 65 37 ) ) PUNCT cana-5883 65 38 is be AUX cana-5883 65 39 an an DET cana-5883 65 40 arbitrary arbitrary ADJ cana-5883 65 41 function function NOUN cana-5883 65 42 of of ADP cana-5883 65 43 the the DET cana-5883 65 44 ricci ricci PROPN cana-5883 65 45 tensor tensor NOUN cana-5883 65 46 r r NOUN cana-5883 65 47 and and CCONJ cana-5883 65 48 energy energy NOUN cana-5883 65 49 momentum momentum NOUN cana-5883 65 50 tensor tensor NOUN cana-5883 65 51 t. t. NOUN cana-5883 65 52 three three NUM cana-5883 65 53 obvious obvious ADJ cana-5883 65 54 requirements requirement NOUN cana-5883 65 55 of of ADP cana-5883 65 56 the the DET cana-5883 65 57 operational operational ADJ cana-5883 65 58 from from ADP cana-5883 65 59 of of ADP cana-5883 65 60 f f PROPN cana-5883 65 61 ( ( PUNCT cana-5883 65 62 r r PROPN cana-5883 65 63 , , PUNCT cana-5883 65 64 t t PROPN cana-5883 65 65 ) ) PUNCT cana-5883 65 66 are be AUX cana-5883 65 67 standardly standardly ADV cana-5883 65 68 considered consider VERB cana-5883 65 69 , , PUNCT cana-5883 65 70 𝑓(𝑅 𝑓(𝑅 NOUN cana-5883 65 71 , , PUNCT cana-5883 65 72 𝑇 𝑇 PROPN cana-5883 65 73 ) ) PUNCT cana-5883 65 74 = = NOUN cana-5883 65 75 { { PUNCT cana-5883 65 76 𝑅 𝑅 NOUN cana-5883 65 77 + + NOUN cana-5883 65 78 2𝑓(𝑇 2𝑓(𝑇 NUM cana-5883 65 79 ) ) PUNCT cana-5883 65 80 𝑓1(𝑅 𝑓1(𝑅 NOUN cana-5883 65 81 ) ) PUNCT cana-5883 66 1 + + SYM cana-5883 66 2 𝑓2(𝑇 𝑓2(𝑇 ADJ cana-5883 66 3 ) ) PUNCT cana-5883 66 4 𝑓1(𝑅 𝑓1(𝑅 NOUN cana-5883 66 5 ) ) PUNCT cana-5883 67 1 + + CCONJ cana-5883 67 2 𝑓2(𝑅)𝑓3(𝑇 𝑓2(𝑅)𝑓3(𝑇 PROPN cana-5883 67 3 ) ) PUNCT cana-5883 67 4 ( ( PUNCT cana-5883 67 5 2 2 X cana-5883 67 6 ) ) PUNCT cana-5883 67 7 assuming assume VERB cana-5883 67 8 as as ADP cana-5883 67 9 a a DET cana-5883 67 10 choice choice NOUN cana-5883 67 11 of of ADP cana-5883 67 12 f f PROPN cana-5883 67 13 ( ( PUNCT cana-5883 67 14 r r PROPN cana-5883 67 15 , , PUNCT cana-5883 67 16 t t PROPN cana-5883 67 17 ) ) PUNCT cana-5883 67 18 = = SYM cana-5883 68 1 f1(r f1(r X cana-5883 68 2 ) ) PUNCT cana-5883 68 3 + + NUM cana-5883 68 4 f2(t f2(t PROPN cana-5883 68 5 ) ) PUNCT cana-5883 68 6 , , PUNCT cana-5883 68 7 where where SCONJ cana-5883 68 8 f1(r f1(r NOUN cana-5883 68 9 ) ) PUNCT cana-5883 68 10 = = SYM cana-5883 68 11 πœ†r πœ†r NOUN cana-5883 68 12 and and CCONJ cana-5883 68 13 f2(t f2(t PROPN cana-5883 68 14 ) ) PUNCT cana-5883 68 15 = = PRON cana-5883 68 16 πœ†t πœ†t PROPN cana-5883 68 17 , , PUNCT cana-5883 68 18 where where SCONJ cana-5883 68 19 πœ† πœ† NOUN cana-5883 68 20 is be AUX cana-5883 68 21 free free ADJ cana-5883 68 22 parameter parameter NOUN cana-5883 68 23 . . PUNCT cana-5883 69 1 therefore therefore ADV cana-5883 69 2 , , PUNCT cana-5883 69 3 equation equation NOUN cana-5883 69 4 ( ( PUNCT cana-5883 69 5 2 2 X cana-5883 69 6 ) ) PUNCT cana-5883 69 7 can can AUX cana-5883 69 8 be be AUX cana-5883 69 9 written write VERB cana-5883 69 10 as as ADP cana-5883 69 11 , , PUNCT cana-5883 69 12 𝑓1 𝑓1 PROPN cana-5883 69 13 β€²(𝑅)𝑅𝑖𝑗 β€²(𝑅)𝑅𝑖𝑗 PROPN cana-5883 69 14 βˆ’ βˆ’ PROPN cana-5883 69 15 1 1 NUM cana-5883 69 16 2 2 NUM cana-5883 69 17 𝑓1(𝑅)𝑔𝑖𝑗 𝑓1(𝑅)𝑔𝑖𝑗 NOUN cana-5883 69 18 + + CCONJ cana-5883 69 19 ( ( PUNCT cana-5883 69 20 𝑔𝑖𝑗 𝑔𝑖𝑗 VERB cana-5883 69 21 βˆ‡π‘–βˆ‡π‘– βˆ‡π‘–βˆ‡π‘– NOUN cana-5883 69 22 βˆ‡π‘–βˆ‡π‘— βˆ‡π‘–βˆ‡π‘— NUM cana-5883 69 23 ) ) PUNCT cana-5883 69 24 𝑓1 𝑓1 PROPN cana-5883 69 25 ( ( PUNCT cana-5883 69 26 𝑅 𝑅 PROPN cana-5883 69 27 ) ) PUNCT cana-5883 69 28 = = PUNCT cana-5883 70 1 k𝑇𝑖𝑗 k𝑇𝑖𝑗 PROPN cana-5883 70 2 βˆ’ βˆ’ PROPN cana-5883 70 3 𝑓2 𝑓2 NOUN cana-5883 70 4 β€²(𝑇 β€²(𝑇 NOUN cana-5883 70 5 ) ) PUNCT cana-5883 71 1 𝑇𝑖𝑗 𝑇𝑖𝑗 NOUN cana-5883 71 2 βˆ’π‘“2 βˆ’π‘“2 NOUN cana-5883 71 3 β€²(𝑇)θ𝑖𝑗 β€²(𝑇)θ𝑖𝑗 NOUN cana-5883 71 4 + + CCONJ cana-5883 71 5 1 1 NUM cana-5883 71 6 2 2 NUM cana-5883 71 7 𝑓2(t)𝑔𝑖𝑗 𝑓2(t)𝑔𝑖𝑗 NOUN cana-5883 71 8 ( ( PUNCT cana-5883 71 9 3 3 X cana-5883 71 10 ) ) PUNCT cana-5883 71 11 communications communication NOUN cana-5883 71 12 on on ADP cana-5883 71 13 applied apply VERB cana-5883 71 14 nonlinear nonlinear ADJ cana-5883 71 15 analysis analysis NOUN cana-5883 71 16 issn issn NOUN cana-5883 71 17 : : PUNCT cana-5883 71 18 1074 1074 NUM cana-5883 71 19 - - PUNCT cana-5883 71 20 133x 133x NUM cana-5883 71 21 vol vol NOUN cana-5883 71 22 32 32 NUM cana-5883 71 23 no no NOUN cana-5883 71 24 . . PUNCT cana-5883 72 1 2s 2s NUM cana-5883 72 2 ( ( PUNCT cana-5883 72 3 2025 2025 NUM cana-5883 72 4 ) ) PUNCT cana-5883 72 5 607 607 NUM cana-5883 72 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 72 7 where where SCONJ cana-5883 72 8 the the DET cana-5883 72 9 prime prime ADJ cana-5883 72 10 denotes denote NOUN cana-5883 72 11 differentiation differentiation NOUN cana-5883 72 12 with with ADP cana-5883 72 13 respect respect NOUN cana-5883 72 14 to to ADP cana-5883 72 15 the the DET cana-5883 72 16 arguments argument NOUN cana-5883 72 17 . . PUNCT cana-5883 73 1 where where SCONJ cana-5883 73 2 θ𝑖𝑗 θ𝑖𝑗 NOUN cana-5883 73 3 is be AUX cana-5883 73 4 expressed express VERB cana-5883 73 5 as as ADP cana-5883 73 6 , , PUNCT cana-5883 73 7 θ𝑖𝑗 θ𝑖𝑗 NOUN cana-5883 73 8 = = PUNCT cana-5883 73 9 π‘”π‘™π‘š π‘”π‘™π‘š NOUN cana-5883 73 10 Ξ΄tlm Ξ΄tlm PROPN cana-5883 73 11 δ𝑔𝑖𝑗 δ𝑔𝑖𝑗 NOUN cana-5883 73 12 ( ( PUNCT cana-5883 73 13 4 4 NUM cana-5883 73 14 ) ) PUNCT cana-5883 73 15 where where SCONJ cana-5883 73 16 tij tij PROPN cana-5883 73 17 is be AUX cana-5883 73 18 energy energy NOUN cana-5883 73 19 momentum momentum NOUN cana-5883 73 20 tensor tensor NOUN cana-5883 73 21 with with ADP cana-5883 73 22 perfect perfect ADJ cana-5883 73 23 fluid fluid NOUN cana-5883 73 24 and and CCONJ cana-5883 73 25 defined define VERB cana-5883 73 26 as as ADP cana-5883 73 27 , , PUNCT cana-5883 73 28 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5883 73 29 = = SYM cana-5883 73 30 ( ( PUNCT cana-5883 73 31 𝜌 𝜌 X cana-5883 73 32 + + X cana-5883 73 33 𝑝 𝑝 NOUN cana-5883 73 34 ) ) PUNCT cana-5883 73 35 u𝑖u𝑗 u𝑖u𝑗 ADJ cana-5883 73 36 βˆ’ βˆ’ PROPN cana-5883 73 37 𝑝𝑔𝑖𝑗 𝑝𝑔𝑖𝑗 NOUN cana-5883 73 38 ( ( PUNCT cana-5883 73 39 5 5 NUM cana-5883 73 40 ) ) PUNCT cana-5883 73 41 where where SCONJ cana-5883 73 42 𝑒𝑖 𝑒𝑖 ADV cana-5883 73 43 = = SYM cana-5883 73 44 ( ( PUNCT cana-5883 73 45 0,0,0,1 0,0,0,1 NOUN cana-5883 73 46 ) ) PUNCT cana-5883 73 47 is be AUX cana-5883 73 48 four four NUM cana-5883 73 49 velocity velocity NOUN cana-5883 73 50 vector vector NOUN cana-5883 73 51 satisfying satisfy VERB cana-5883 73 52 𝑒𝑖𝑒𝑗 𝑒𝑖𝑒𝑗 NOUN cana-5883 73 53 = = SYM cana-5883 73 54 1 1 NUM cana-5883 73 55 ( ( PUNCT cana-5883 73 56 6 6 NUM cana-5883 73 57 ) ) PUNCT cana-5883 73 58 p p NOUN cana-5883 73 59 and and CCONJ cana-5883 73 60 𝜌 𝜌 NOUN cana-5883 73 61 are be AUX cana-5883 73 62 pressure pressure NOUN cana-5883 73 63 and and CCONJ cana-5883 73 64 energy energy NOUN cana-5883 73 65 density density NOUN cana-5883 73 66 of of ADP cana-5883 73 67 the the DET cana-5883 73 68 matter matter NOUN cana-5883 73 69 respectively respectively ADV cana-5883 73 70 . . PUNCT cana-5883 74 1 assuming assume VERB cana-5883 74 2 that that SCONJ cana-5883 74 3 the the DET cana-5883 74 4 matter matter NOUN cana-5883 74 5 content content NOUN cana-5883 74 6 consists consist VERB cana-5883 74 7 of of ADP cana-5883 74 8 a a DET cana-5883 74 9 perfect perfect ADJ cana-5883 74 10 fluid fluid NOUN cana-5883 74 11 and and CCONJ cana-5883 74 12 defined define VERB cana-5883 74 13 as as ADP cana-5883 74 14 , , PUNCT cana-5883 74 15 θ𝑖𝑗 θ𝑖𝑗 NOUN cana-5883 74 16 = = SYM cana-5883 74 17 βˆ’2 βˆ’2 NOUN cana-5883 74 18 𝑇𝑖𝑗 𝑇𝑖𝑗 NOUN cana-5883 74 19 βˆ’ βˆ’ PROPN cana-5883 74 20 𝑝gij 𝑝gij NOUN cana-5883 74 21 ( ( PUNCT cana-5883 74 22 7 7 X cana-5883 74 23 ) ) PUNCT cana-5883 74 24 the the DET cana-5883 74 25 field field NOUN cana-5883 74 26 equation equation NOUN cana-5883 74 27 takes take VERB cana-5883 74 28 the the DET cana-5883 74 29 form form NOUN cana-5883 74 30 , , PUNCT cana-5883 74 31 λ𝑅𝑖𝑗 λ𝑅𝑖𝑗 PROPN cana-5883 74 32 βˆ’ βˆ’ PROPN cana-5883 74 33 1 1 NUM cana-5883 74 34 2 2 NUM cana-5883 74 35 Ξ»(𝑅 Ξ»(𝑅 NUM cana-5883 74 36 + + CCONJ cana-5883 74 37 𝑇)𝑔𝑖𝑗 𝑇)𝑔𝑖𝑗 NUM cana-5883 74 38 + + CCONJ cana-5883 74 39 ( ( PUNCT cana-5883 74 40 𝑔𝑖𝑗 𝑔𝑖𝑗 VERB cana-5883 74 41 βˆ‡π‘–βˆ‡π‘– βˆ‡π‘–βˆ‡π‘– NOUN cana-5883 74 42 βˆ‡π‘–βˆ‡π‘— βˆ‡π‘–βˆ‡π‘— NUM cana-5883 74 43 ) ) PUNCT cana-5883 74 44 Ξ» Ξ» NOUN cana-5883 74 45 = = SYM cana-5883 74 46 k𝑇𝑖𝑗 k𝑇𝑖𝑗 PROPN cana-5883 74 47 βˆ’ βˆ’ PROPN cana-5883 74 48 Ξ» Ξ» PROPN cana-5883 74 49 𝑇𝑖𝑗 𝑇𝑖𝑗 NOUN cana-5883 74 50 + + PROPN cana-5883 74 51 Ξ» Ξ» PROPN cana-5883 74 52 [ [ PUNCT cana-5883 74 53 2𝑇𝑖𝑗 2𝑇𝑖𝑗 NUM cana-5883 74 54 + + CCONJ cana-5883 74 55 1 1 NUM cana-5883 74 56 2 2 NUM cana-5883 74 57 𝑔𝑖𝑗 𝑔𝑖𝑗 NOUN cana-5883 74 58 ) ) PUNCT cana-5883 74 59 ] ] PUNCT cana-5883 75 1 ( ( PUNCT cana-5883 75 2 8) 8) NUM cana-5883 75 3 generally generally ADV cana-5883 75 4 , , PUNCT cana-5883 75 5 the the DET cana-5883 75 6 field field NOUN cana-5883 75 7 equations equation NOUN cana-5883 75 8 also also ADV cana-5883 75 9 pivot pivot VERB cana-5883 75 10 on on ADP cana-5883 75 11 the the DET cana-5883 75 12 whole whole ADJ cana-5883 75 13 time time NOUN cana-5883 75 14 the the DET cana-5883 75 15 tensor tensor NOUN cana-5883 75 16 πœƒπ‘–π‘— πœƒπ‘–π‘— NOUN cana-5883 75 17 , , PUNCT cana-5883 75 18 on on ADP cana-5883 75 19 the the DET cana-5883 75 20 physical physical ADJ cana-5883 75 21 nature nature NOUN cana-5883 75 22 of of ADP cana-5883 75 23 the the DET cana-5883 75 24 matter matter NOUN cana-5883 75 25 field field NOUN cana-5883 75 26 . . PUNCT cana-5883 76 1 hence hence ADV cana-5883 76 2 in in ADP cana-5883 76 3 the the DET cana-5883 76 4 case case NOUN cana-5883 76 5 of of ADP cana-5883 76 6 f f PROPN cana-5883 76 7 ( ( PUNCT cana-5883 76 8 r r PROPN cana-5883 76 9 , , PUNCT cana-5883 76 10 t t NOUN cana-5883 76 11 ) ) PUNCT cana-5883 76 12 gravity gravity NOUN cana-5883 76 13 depending depend VERB cana-5883 76 14 on on ADP cana-5883 76 15 the the DET cana-5883 76 16 nature nature NOUN cana-5883 76 17 of of ADP cana-5883 76 18 the the DET cana-5883 76 19 matter matter NOUN cana-5883 76 20 source source NOUN cana-5883 76 21 , , PUNCT cana-5883 76 22 we we PRON cana-5883 76 23 prevailed prevail VERB cana-5883 76 24 several several ADJ cana-5883 76 25 theoretical theoretical ADJ cana-5883 76 26 models model NOUN cana-5883 76 27 corresponding correspond VERB cana-5883 76 28 to to ADP cana-5883 76 29 each each DET cana-5883 76 30 choice choice NOUN cana-5883 76 31 of of ADP cana-5883 76 32 f f PROPN cana-5883 76 33 ( ( PUNCT cana-5883 76 34 r r PROPN cana-5883 76 35 , , PUNCT cana-5883 76 36 t t PROPN cana-5883 76 37 ) ) PUNCT cana-5883 76 38 . . PUNCT cana-5883 77 1 out out ADP cana-5883 77 2 of of ADP cana-5883 77 3 three three NUM cana-5883 77 4 explicit explicit ADJ cana-5883 77 5 specifications specification NOUN cana-5883 77 6 of of ADP cana-5883 77 7 the the DET cana-5883 77 8 functional functional ADJ cana-5883 77 9 form form NOUN cana-5883 77 10 of of ADP cana-5883 77 11 f f PROPN cana-5883 77 12 ( ( PUNCT cana-5883 77 13 r r PROPN cana-5883 77 14 , , PUNCT cana-5883 77 15 t t PROPN cana-5883 77 16 ) ) PUNCT cana-5883 77 17 . . PUNCT cana-5883 78 1 now now ADV cana-5883 78 2 , , PUNCT cana-5883 78 3 we we PRON cana-5883 78 4 have have VERB cana-5883 78 5 𝑅𝑖𝑗 𝑅𝑖𝑗 PROPN cana-5883 78 6 βˆ’ βˆ’ NOUN cana-5883 78 7 1 1 NUM cana-5883 78 8 2 2 NUM cana-5883 78 9 𝑅𝑔𝑖𝑗 𝑅𝑔𝑖𝑗 PROPN cana-5883 78 10 βˆ’ βˆ’ PROPN cana-5883 78 11 ( ( PUNCT cana-5883 78 12 𝑝 𝑝 PROPN cana-5883 78 13 + + CCONJ cana-5883 78 14 1 1 NUM cana-5883 78 15 2 2 NUM cana-5883 78 16 𝑇)𝑔𝑖𝑗 𝑇)𝑔𝑖𝑗 NUM cana-5883 78 17 = = PUNCT cana-5883 78 18 ( ( PUNCT cana-5883 78 19 k+Ξ» k+Ξ» X cana-5883 78 20 Ξ» Ξ» X cana-5883 78 21 ) ) PUNCT cana-5883 79 1 𝑇𝑖𝑗 𝑇𝑖𝑗 PROPN cana-5883 79 2 ( ( PUNCT cana-5883 79 3 9 9 NUM cana-5883 79 4 ) ) PUNCT cana-5883 79 5 recollecting recollect VERB cana-5883 79 6 einstein einstein PROPN cana-5883 79 7 equations equation NOUN cana-5883 79 8 inclusive inclusive ADJ cana-5883 79 9 of of ADP cana-5883 79 10 cosmological cosmological ADJ cana-5883 79 11 constant constant ADJ cana-5883 79 12 , , PUNCT cana-5883 79 13 𝐺𝑖𝑗 𝐺𝑖𝑗 PROPN cana-5883 79 14 βˆ’ βˆ’ NOUN cana-5883 79 15 λ𝑔𝑖𝑗 λ𝑔𝑖𝑗 NOUN cana-5883 79 16 = = PUNCT cana-5883 80 1 βˆ’ βˆ’ PROPN cana-5883 80 2 k𝑇𝑖𝑗 k𝑇𝑖𝑗 PROPN cana-5883 80 3 ( ( PUNCT cana-5883 80 4 10 10 NUM cana-5883 80 5 ) ) PUNCT cana-5883 80 6 pick pick VERB cana-5883 80 7 out out ADP cana-5883 80 8 k=1 k=1 X cana-5883 80 9 . . PUNCT cana-5883 81 1 we we PRON cana-5883 81 2 choose choose VERB cana-5883 81 3 a a DET cana-5883 81 4 negative negative ADJ cana-5883 81 5 small small ADJ cana-5883 81 6 value value NOUN cana-5883 81 7 for for ADP cana-5883 81 8 the the DET cana-5883 81 9 arbitrary arbitrary ADJ cana-5883 81 10 Ξ» Ξ» NOUN cana-5883 81 11 , , PUNCT cana-5883 81 12 so so SCONJ cana-5883 81 13 that that SCONJ cana-5883 81 14 we we PRON cana-5883 81 15 have have VERB cana-5883 81 16 the the DET cana-5883 81 17 same same ADJ cana-5883 81 18 sign sign NOUN cana-5883 81 19 of of ADP cana-5883 81 20 the the DET cana-5883 81 21 rhs rhs PROPN cana-5883 81 22 . . PUNCT cana-5883 82 1 of of ADP cana-5883 82 2 ( ( PUNCT cana-5883 82 3 9 9 NUM cana-5883 82 4 ) ) PUNCT cana-5883 82 5 and and CCONJ cana-5883 82 6 ( ( PUNCT cana-5883 82 7 10 10 NUM cana-5883 82 8 ) ) PUNCT cana-5883 82 9 , , PUNCT cana-5883 82 10 we we PRON cana-5883 82 11 keep keep VERB cana-5883 82 12 this this DET cana-5883 82 13 choice choice NOUN cana-5883 82 14 of of ADP cana-5883 82 15 Ξ» Ξ» NOUN cana-5883 82 16 throughout throughout ADP cana-5883 82 17 . . PUNCT cana-5883 83 1 ( ( PUNCT cana-5883 83 2 p p NOUN cana-5883 83 3 + + NOUN cana-5883 83 4 1 1 NUM cana-5883 83 5 2 2 NUM cana-5883 83 6 t t NOUN cana-5883 83 7 ) ) PUNCT cana-5883 83 8 can can AUX cana-5883 83 9 be be AUX cana-5883 83 10 regarded regard VERB cana-5883 83 11 now now ADV cana-5883 83 12 as as ADP cana-5883 83 13 a a DET cana-5883 83 14 cosmological cosmological ADJ cana-5883 83 15 constant constant ADJ cana-5883 83 16 term term NOUN cana-5883 83 17 t. t. PROPN cana-5883 83 18 hence hence ADV cana-5883 83 19 , , PUNCT cana-5883 83 20 we we PRON cana-5883 83 21 can can AUX cana-5883 83 22 write write VERB cana-5883 83 23 , , PUNCT cana-5883 83 24 Ξ»(t Ξ»(t X cana-5883 83 25 ) ) PUNCT cana-5883 84 1 = = SYM cana-5883 85 1 p p NOUN cana-5883 85 2 + + NOUN cana-5883 85 3 1 1 NUM cana-5883 85 4 2 2 NUM cana-5883 85 5 𝑇 𝑇 NOUN cana-5883 85 6 ( ( PUNCT cana-5883 85 7 11 11 NUM cana-5883 85 8 ) ) PUNCT cana-5883 85 9 hence hence ADV cana-5883 85 10 eq eq NOUN cana-5883 85 11 . . PUNCT cana-5883 86 1 ( ( PUNCT cana-5883 86 2 11 11 NUM cana-5883 86 3 ) ) PUNCT cana-5883 86 4 reduces reduce VERB cana-5883 86 5 to to ADP cana-5883 86 6 , , PUNCT cana-5883 86 7 communications communication NOUN cana-5883 86 8 on on ADP cana-5883 86 9 applied apply VERB cana-5883 86 10 nonlinear nonlinear ADJ cana-5883 86 11 analysis analysis NOUN cana-5883 86 12 issn issn NOUN cana-5883 86 13 : : PUNCT cana-5883 86 14 1074 1074 NUM cana-5883 86 15 - - PUNCT cana-5883 86 16 133x 133x NUM cana-5883 86 17 vol vol NOUN cana-5883 86 18 32 32 NUM cana-5883 86 19 no no NOUN cana-5883 86 20 . . PUNCT cana-5883 87 1 2s 2s NUM cana-5883 87 2 ( ( PUNCT cana-5883 87 3 2025 2025 NUM cana-5883 87 4 ) ) PUNCT cana-5883 87 5 608 608 NUM cana-5883 87 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 87 7 Ξ»(t Ξ»(t NOUN cana-5883 87 8 ) ) PUNCT cana-5883 87 9 = = SYM cana-5883 87 10 1 1 NUM cana-5883 87 11 2 2 NUM cana-5883 87 12 ( ( PUNCT cana-5883 87 13 ρ ρ NOUN cana-5883 87 14 βˆ’ βˆ’ PROPN cana-5883 87 15 p p NOUN cana-5883 87 16 ) ) PUNCT cana-5883 87 17 ( ( PUNCT cana-5883 87 18 12 12 NUM cana-5883 87 19 ) ) PUNCT cana-5883 87 20 iii iii PROPN cana-5883 87 21 . . PUNCT cana-5883 87 22 gravitational gravitational ADJ cana-5883 87 23 field field NOUN cana-5883 87 24 equation equation NOUN cana-5883 87 25 we we PRON cana-5883 87 26 consider consider VERB cana-5883 87 27 a a DET cana-5883 87 28 homogeneous homogeneous ADJ cana-5883 87 29 bianchi bianchi NOUN cana-5883 87 30 type type NOUN cana-5883 87 31 – – PUNCT cana-5883 87 32 v v NOUN cana-5883 87 33 metric metric NOUN cana-5883 87 34 , , PUNCT cana-5883 87 35 which which PRON cana-5883 87 36 is be AUX cana-5883 87 37 given give VERB cana-5883 87 38 by by ADP cana-5883 87 39 , , PUNCT cana-5883 87 40 𝑑𝑠2= 𝑑𝑠2= VERB cana-5883 87 41 𝑑𝑑2 𝑑𝑑2 NOUN cana-5883 87 42 βˆ’ βˆ’ PROPN cana-5883 87 43 π‘Ž1 π‘Ž1 PROPN cana-5883 87 44 2𝑑π‘₯2 2𝑑π‘₯2 NUM cana-5883 87 45 βˆ’ βˆ’ PROPN cana-5883 87 46 𝑒2π‘šπ‘₯[π‘Ž2 𝑒2π‘šπ‘₯[π‘Ž2 PROPN cana-5883 87 47 2𝑑𝑦2 2𝑑𝑦2 NUM cana-5883 87 48 + + CCONJ cana-5883 87 49 π‘Ž3 π‘Ž3 PROPN cana-5883 87 50 2𝑑𝑧2 2𝑑𝑧2 NUM cana-5883 87 51 ] ] X cana-5883 87 52 ( ( PUNCT cana-5883 87 53 13 13 NUM cana-5883 87 54 ) ) PUNCT cana-5883 87 55 where where SCONJ cana-5883 87 56 , , PUNCT cana-5883 87 57 a a DET cana-5883 87 58 , , PUNCT cana-5883 87 59 b b NOUN cana-5883 87 60 and and CCONJ cana-5883 87 61 c c PROPN cana-5883 87 62 are be AUX cana-5883 87 63 functions function NOUN cana-5883 87 64 of of ADP cana-5883 87 65 cosmic cosmic ADJ cana-5883 87 66 time time NOUN cana-5883 87 67 t t NOUN cana-5883 87 68 only only ADV cana-5883 87 69 . . PUNCT cana-5883 88 1 now now ADV cana-5883 88 2 assuming assume VERB cana-5883 88 3 commoving commoving ADJ cana-5883 88 4 coordinate coordinate NOUN cana-5883 88 5 system system NOUN cana-5883 88 6 , , PUNCT cana-5883 88 7 the the DET cana-5883 88 8 field field NOUN cana-5883 88 9 equation equation NOUN cana-5883 88 10 ( ( PUNCT cana-5883 88 11 9 9 NUM cana-5883 88 12 ) ) PUNCT cana-5883 88 13 with with ADP cana-5883 88 14 the the DET cana-5883 88 15 help help NOUN cana-5883 88 16 of of ADP cana-5883 88 17 ( ( PUNCT cana-5883 88 18 5 5 NUM cana-5883 88 19 ) ) PUNCT cana-5883 88 20 and and CCONJ cana-5883 88 21 ( ( PUNCT cana-5883 88 22 6 6 NUM cana-5883 88 23 ) ) PUNCT cana-5883 88 24 for for ADP cana-5883 88 25 the the DET cana-5883 88 26 metric metric ADJ cana-5883 88 27 ( ( PUNCT cana-5883 88 28 12 12 NUM cana-5883 88 29 ) ) PUNCT cana-5883 88 30 can can AUX cana-5883 88 31 be be AUX cana-5883 88 32 written write VERB cana-5883 88 33 as as ADP cana-5883 88 34 , , PUNCT cana-5883 88 35 π‘Ž2Μ‡π‘Ž3Μ‡ π‘Ž2Μ‡π‘Ž3Μ‡ NOUN cana-5883 88 36 π‘Ž2π‘Ž3 π‘Ž2π‘Ž3 ADV cana-5883 88 37 + + CCONJ cana-5883 88 38 π‘Ž3̈ π‘Ž3̈ PROPN cana-5883 88 39 π‘Ž3 π‘Ž3 PROPN cana-5883 88 40 + + CCONJ cana-5883 88 41 π‘Ž2̈ π‘Ž2̈ PROPN cana-5883 88 42 π‘Ž2 π‘Ž2 NOUN cana-5883 88 43 βˆ’ βˆ’ PROPN cana-5883 88 44 π‘š π‘š NOUN cana-5883 88 45 π‘Ž1 π‘Ž1 PROPN cana-5883 88 46 2 2 NUM cana-5883 88 47 = = SYM cana-5883 88 48 ( ( PUNCT cana-5883 88 49 8Ο€+Ξ» 8Ο€+Ξ» NUM cana-5883 88 50 Ξ» Ξ» NOUN cana-5883 88 51 ) ) PUNCT cana-5883 88 52 p p NOUN cana-5883 88 53 Ξ» Ξ» PROPN cana-5883 88 54 ( ( PUNCT cana-5883 88 55 14 14 NUM cana-5883 88 56 ) ) PUNCT cana-5883 88 57 π‘Ž1Μ‡π‘Ž3Μ‡ π‘Ž1Μ‡π‘Ž3Μ‡ NOUN cana-5883 88 58 π‘Ž1π‘Ž3 π‘Ž1π‘Ž3 X cana-5883 88 59 + + NUM cana-5883 88 60 π‘Ž1̈ π‘Ž1̈ NOUN cana-5883 88 61 π‘Ž1 π‘Ž1 NOUN cana-5883 88 62 + + CCONJ cana-5883 88 63 π‘Ž3̈ π‘Ž3̈ PROPN cana-5883 88 64 π‘Ž3 π‘Ž3 PROPN cana-5883 88 65 βˆ’ βˆ’ PROPN cana-5883 89 1 π‘š π‘š PROPN cana-5883 89 2 π‘Ž1 π‘Ž1 NOUN cana-5883 89 3 2 2 NUM cana-5883 89 4 = = SYM cana-5883 89 5 ( ( PUNCT cana-5883 89 6 8Ο€+Ξ» 8Ο€+Ξ» NUM cana-5883 89 7 Ξ» Ξ» NOUN cana-5883 89 8 ) ) PUNCT cana-5883 89 9 p p NOUN cana-5883 89 10 Ξ» Ξ» PROPN cana-5883 89 11 ( ( PUNCT cana-5883 89 12 15 15 NUM cana-5883 89 13 ) ) PUNCT cana-5883 89 14 π‘Ž1Μ‡π‘Ž2Μ‡ π‘Ž1Μ‡π‘Ž2Μ‡ NOUN cana-5883 89 15 π‘Ž1π‘Ž2 π‘Ž1π‘Ž2 X cana-5883 89 16 + + NUM cana-5883 89 17 π‘Ž1̈ π‘Ž1̈ NOUN cana-5883 89 18 π‘Ž1 π‘Ž1 NOUN cana-5883 89 19 + + CCONJ cana-5883 89 20 π‘Ž2̈ π‘Ž2̈ PROPN cana-5883 89 21 π‘Ž2 π‘Ž2 NOUN cana-5883 89 22 βˆ’ βˆ’ PROPN cana-5883 89 23 π‘š π‘š NOUN cana-5883 89 24 π‘Ž1 π‘Ž1 PROPN cana-5883 89 25 2 2 NUM cana-5883 89 26 = = SYM cana-5883 89 27 ( ( PUNCT cana-5883 89 28 8Ο€+Ξ» 8Ο€+Ξ» NUM cana-5883 89 29 Ξ» Ξ» NOUN cana-5883 89 30 ) ) PUNCT cana-5883 89 31 p p NOUN cana-5883 89 32 – – PUNCT cana-5883 89 33 Ξ» Ξ» X cana-5883 89 34 ( ( PUNCT cana-5883 89 35 16 16 NUM cana-5883 89 36 ) ) PUNCT cana-5883 89 37 π‘Ž1Μ‡ π‘Ž1Μ‡ NOUN cana-5883 90 1 π‘Ž1 π‘Ž1 NOUN cana-5883 90 2 π‘Ž2Μ‡ π‘Ž2Μ‡ PROPN cana-5883 90 3 π‘Ž2 π‘Ž2 NOUN cana-5883 90 4 + + CCONJ cana-5883 90 5 π‘Ž2π‘Ž3Μ‡ π‘Ž2π‘Ž3Μ‡ AUX cana-5883 90 6 Μ‡ Μ‡ VERB cana-5883 90 7 π‘Ž2π‘Ž3 π‘Ž2π‘Ž3 ADV cana-5883 90 8 + + PUNCT cana-5883 90 9 π‘Ž1Μ‡π‘Ž3Μ‡ π‘Ž1Μ‡π‘Ž3Μ‡ NOUN cana-5883 90 10 π‘Ž1π‘Ž3 π‘Ž1π‘Ž3 X cana-5883 90 11 βˆ’ βˆ’ PROPN cana-5883 91 1 3π‘š 3π‘š NUM cana-5883 91 2 π‘Ž1 π‘Ž1 NOUN cana-5883 91 3 2 2 NUM cana-5883 91 4 = = SYM cana-5883 91 5 ( ( PUNCT cana-5883 91 6 8Ο€+Ξ» 8Ο€+Ξ» NUM cana-5883 91 7 Ξ» Ξ» NOUN cana-5883 91 8 ) ) PUNCT cana-5883 91 9 𝜌λ 𝜌λ PROPN cana-5883 91 10 ( ( PUNCT cana-5883 91 11 17 17 NUM cana-5883 91 12 ) ) SYM cana-5883 91 13 2 2 NUM cana-5883 91 14 π‘Ž1Μ‡ π‘Ž1Μ‡ NOUN cana-5883 92 1 π‘Ž1 π‘Ž1 NOUN cana-5883 92 2 βˆ’ βˆ’ PROPN cana-5883 92 3 π‘Ž2Μ‡ π‘Ž2Μ‡ NOUN cana-5883 92 4 π‘Ž2 π‘Ž2 NOUN cana-5883 92 5 βˆ’ βˆ’ PROPN cana-5883 92 6 π‘Ž3Μ‡ π‘Ž3Μ‡ NOUN cana-5883 92 7 π‘Ž3 π‘Ž3 NOUN cana-5883 92 8 = = SYM cana-5883 92 9 0 0 NUM cana-5883 92 10 ( ( PUNCT cana-5883 92 11 18 18 NUM cana-5883 92 12 ) ) PUNCT cana-5883 92 13 from from ADP cana-5883 92 14 equations equation NOUN cana-5883 92 15 ( ( PUNCT cana-5883 92 16 14)-(16 14)-(16 NOUN cana-5883 92 17 ) ) PUNCT cana-5883 92 18 together together ADV cana-5883 92 19 with with ADP cana-5883 92 20 equation equation NOUN cana-5883 92 21 ( ( PUNCT cana-5883 92 22 17 17 NUM cana-5883 92 23 ) ) PUNCT cana-5883 92 24 , , PUNCT cana-5883 92 25 we we PRON cana-5883 92 26 get get VERB cana-5883 92 27 – – PUNCT cana-5883 92 28 π‘Ž1Μ‡ π‘Ž1Μ‡ VERB cana-5883 92 29 π‘Ž1 π‘Ž1 NOUN cana-5883 92 30 = = PUNCT cana-5883 92 31 aΜ‡ aΜ‡ PROPN cana-5883 92 32 a a DET cana-5883 92 33 ( ( PUNCT cana-5883 92 34 19 19 NUM cana-5883 92 35 ) ) PUNCT cana-5883 92 36 π‘Ž2Μ‡ π‘Ž2Μ‡ NOUN cana-5883 92 37 π‘Ž2 π‘Ž2 NOUN cana-5883 92 38 = = PUNCT cana-5883 92 39 aΜ‡ aΜ‡ PROPN cana-5883 92 40 a a PRON cana-5883 92 41 – – PUNCT cana-5883 92 42 π‘˜ π‘˜ PRON cana-5883 92 43 a3 a3 NOUN cana-5883 92 44 ( ( PUNCT cana-5883 92 45 20 20 NUM cana-5883 92 46 ) ) PUNCT cana-5883 92 47 π‘Ž3Μ‡ π‘Ž3Μ‡ NOUN cana-5883 92 48 π‘Ž3 π‘Ž3 PROPN cana-5883 92 49 = = PROPN cana-5883 92 50 aΜ‡ aΜ‡ PROPN cana-5883 92 51 a a PRON cana-5883 92 52 + + X cana-5883 92 53 π‘˜ π‘˜ DET cana-5883 92 54 a3 a3 NOUN cana-5883 92 55 ( ( PUNCT cana-5883 92 56 21 21 NUM cana-5883 92 57 ) ) PUNCT cana-5883 92 58 where where SCONJ cana-5883 92 59 π‘˜ π‘˜ NOUN cana-5883 92 60 is be AUX cana-5883 92 61 constant constant ADJ cana-5883 92 62 . . PUNCT cana-5883 93 1 the the DET cana-5883 93 2 spatial spatial ADJ cana-5883 93 3 volume volume NOUN cana-5883 93 4 and and CCONJ cana-5883 93 5 the the DET cana-5883 93 6 scale scale NOUN cana-5883 93 7 factor factor NOUN cana-5883 93 8 of of ADP cana-5883 93 9 the the DET cana-5883 93 10 metric metric ADJ cana-5883 93 11 ( ( PUNCT cana-5883 93 12 13 13 NUM cana-5883 93 13 ) ) PUNCT cana-5883 93 14 are be AUX cana-5883 93 15 defined define VERB cana-5883 93 16 by by ADP cana-5883 93 17 , , PUNCT cana-5883 93 18 𝑉 𝑉 PROPN cana-5883 93 19 = = SYM cana-5883 93 20 π‘Ž3 π‘Ž3 PROPN cana-5883 93 21 = = SYM cana-5883 93 22 π‘Ž1π‘Ž2π‘Ž3 π‘Ž1π‘Ž2π‘Ž3 PROPN cana-5883 93 23 ( ( PUNCT cana-5883 93 24 22 22 NUM cana-5883 93 25 ) ) PUNCT cana-5883 93 26 the the DET cana-5883 93 27 physical physical ADJ cana-5883 93 28 quantities quantity NOUN cana-5883 93 29 of of ADP cana-5883 93 30 observational observational ADJ cana-5883 93 31 interest interest NOUN cana-5883 93 32 in in ADP cana-5883 93 33 cosmology cosmology NOUN cana-5883 93 34 are be AUX cana-5883 93 35 as as ADP cana-5883 93 36 ; ; PUNCT cana-5883 93 37 the the DET cana-5883 93 38 mean mean ADJ cana-5883 93 39 generalized generalized ADJ cana-5883 93 40 hubble hubble ADJ cana-5883 93 41 parameter parameter NOUN cana-5883 93 42 becomes become VERB cana-5883 93 43 , , PUNCT cana-5883 93 44 communications communication NOUN cana-5883 93 45 on on ADP cana-5883 93 46 applied apply VERB cana-5883 93 47 nonlinear nonlinear ADJ cana-5883 93 48 analysis analysis NOUN cana-5883 93 49 issn issn NOUN cana-5883 93 50 : : PUNCT cana-5883 93 51 1074 1074 NUM cana-5883 93 52 - - PUNCT cana-5883 93 53 133x 133x NUM cana-5883 93 54 vol vol NOUN cana-5883 93 55 32 32 NUM cana-5883 93 56 no no NOUN cana-5883 93 57 . . PUNCT cana-5883 94 1 2s 2s NUM cana-5883 94 2 ( ( PUNCT cana-5883 94 3 2025 2025 NUM cana-5883 94 4 ) ) PUNCT cana-5883 94 5 609 609 NUM cana-5883 94 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 94 7 h h NOUN cana-5883 94 8 = = PUNCT cana-5883 94 9 aΜ‡ aΜ‡ PROPN cana-5883 94 10 a a PRON cana-5883 94 11 = = SYM cana-5883 94 12 1 1 NUM cana-5883 94 13 3 3 NUM cana-5883 94 14 ( ( PUNCT cana-5883 94 15 π‘Ž1Μ‡ π‘Ž1Μ‡ VERB cana-5883 94 16 π‘Ž1 π‘Ž1 NOUN cana-5883 94 17 + + CCONJ cana-5883 94 18 π‘Ž2Μ‡ π‘Ž2Μ‡ PROPN cana-5883 94 19 π‘Ž2 π‘Ž2 NOUN cana-5883 94 20 + + CCONJ cana-5883 94 21 π‘Ž3Μ‡ π‘Ž3Μ‡ PROPN cana-5883 94 22 π‘Ž3 π‘Ž3 PROPN cana-5883 94 23 ) ) PUNCT cana-5883 94 24 ( ( PUNCT cana-5883 94 25 23 23 NUM cana-5883 94 26 ) ) PUNCT cana-5883 94 27 the the DET cana-5883 94 28 energy energy NOUN cana-5883 94 29 density density NOUN cana-5883 94 30 , , PUNCT cana-5883 94 31 pressure pressure NOUN cana-5883 94 32 and and CCONJ cana-5883 94 33 cosmological cosmological ADJ cana-5883 94 34 term term NOUN cana-5883 94 35 for for ADP cana-5883 94 36 this this DET cana-5883 94 37 model model NOUN cana-5883 94 38 are be AUX cana-5883 94 39 demonstrates demonstrate VERB cana-5883 94 40 as as ADP cana-5883 94 41 , , PUNCT cana-5883 94 42 𝜌 𝜌 X cana-5883 94 43 = = SYM cana-5883 94 44 2πœ†2 2πœ†2 NUM cana-5883 95 1 [ [ X cana-5883 95 2 ( ( PUNCT cana-5883 95 3 8Ο€+3Ξ»)2βˆ’Ξ»2 8Ο€+3Ξ»)2βˆ’Ξ»2 NUM cana-5883 95 4 [ [ PUNCT cana-5883 95 5 οΏ½ οΏ½ PROPN cana-5883 95 6 Μ‡ Μ‡ PROPN cana-5883 95 7 οΏ½ οΏ½ PROPN cana-5883 95 8 βˆ’ βˆ’ PROPN cana-5883 95 9 3(8Ο€+Ξ» 3(8Ο€+Ξ» NUM cana-5883 95 10 ) ) PUNCT cana-5883 96 1 Ξ» Ξ» NOUN cana-5883 96 2 𝐻2 𝐻2 VERB cana-5883 96 3 + + CCONJ cana-5883 96 4 ( ( PUNCT cana-5883 96 5 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 96 6 ) ) PUNCT cana-5883 96 7 k2 k2 PROPN cana-5883 96 8 Ξ»π‘Ž6 Ξ»π‘Ž6 PROPN cana-5883 97 1 + + CCONJ cana-5883 97 2 ( ( PUNCT cana-5883 97 3 24Ο€+4Ξ» 24Ο€+4Ξ» NUM cana-5883 97 4 ) ) PUNCT cana-5883 97 5 Ξ» Ξ» NOUN cana-5883 97 6 π‘Ž2 π‘Ž2 NOUN cana-5883 97 7 ] ] PUNCT cana-5883 97 8 ( ( PUNCT cana-5883 97 9 24 24 NUM cana-5883 97 10 ) ) PUNCT cana-5883 97 11 p p NOUN cana-5883 97 12 = = SYM cana-5883 97 13 2Ξ»2 2Ξ»2 NUM cana-5883 98 1 [ [ X cana-5883 98 2 ( ( PUNCT cana-5883 98 3 8Ο€+3Ξ»)2 8Ο€+3Ξ»)2 NUM cana-5883 98 4 βˆ’Ξ»2 βˆ’Ξ»2 NOUN cana-5883 98 5 ] ] X cana-5883 98 6 [ [ PUNCT cana-5883 98 7 ( ( PUNCT cana-5883 98 8 16πœ‹+3Ξ» 16πœ‹+3Ξ» NUM cana-5883 98 9 ) ) PUNCT cana-5883 98 10 Ξ» Ξ» NOUN cana-5883 98 11 𝐻 𝐻 NOUN cana-5883 98 12 Μ‡ Μ‡ VERB cana-5883 98 13 + + CCONJ cana-5883 98 14 3(8Ο€+Ξ» 3(8Ο€+Ξ» ADJ cana-5883 98 15 ) ) PUNCT cana-5883 98 16 Ξ» Ξ» NOUN cana-5883 98 17 𝐻2 𝐻2 VERB cana-5883 98 18 + + CCONJ cana-5883 98 19 ( ( PUNCT cana-5883 98 20 8Ο€+2Ξ»)π‘˜2 8Ο€+2Ξ»)π‘˜2 NUM cana-5883 98 21 Ξ»π‘Ž6 Ξ»π‘Ž6 X cana-5883 98 22 βˆ’ βˆ’ NUM cana-5883 98 23 8πœ‹Ξ» 8πœ‹Ξ» ADJ cana-5883 98 24 π‘Ž2 π‘Ž2 NOUN cana-5883 98 25 ] ] PUNCT cana-5883 98 26 ( ( PUNCT cana-5883 98 27 25 25 NUM cana-5883 98 28 ) ) PUNCT cana-5883 98 29 and and CCONJ cana-5883 98 30 ʌ ʌ X cana-5883 98 31 = = SYM cana-5883 98 32 Ξ»2 Ξ»2 PROPN cana-5883 99 1 [ [ X cana-5883 99 2 ( ( PUNCT cana-5883 99 3 8Ο€+3Ξ»)2 8Ο€+3Ξ»)2 NUM cana-5883 99 4 βˆ’Ξ»2 βˆ’Ξ»2 NOUN cana-5883 99 5 ] ] X cana-5883 99 6 [ [ PUNCT cana-5883 99 7 ( ( PUNCT cana-5883 99 8 16πœ‹+2Ξ» 16πœ‹+2Ξ» NUM cana-5883 99 9 ) ) PUNCT cana-5883 99 10 Ξ» Ξ» NOUN cana-5883 99 11 𝐻 𝐻 NOUN cana-5883 99 12 Μ‡ Μ‡ VERB cana-5883 99 13 βˆ’ βˆ’ NOUN cana-5883 99 14 6(8πœ‹+Ξ» 6(8πœ‹+Ξ» NOUN cana-5883 99 15 ) ) PUNCT cana-5883 99 16 Ξ» Ξ» NOUN cana-5883 99 17 𝐻2 𝐻2 VERB cana-5883 99 18 + + CCONJ cana-5883 99 19 ( ( PUNCT cana-5883 99 20 32πœ‹+4Ξ» 32πœ‹+4Ξ» NUM cana-5883 99 21 ) ) PUNCT cana-5883 99 22 π‘Ž2 π‘Ž2 PROPN cana-5883 99 23 Ξ» Ξ» PROPN cana-5883 99 24 ] ] X cana-5883 99 25 ( ( PUNCT cana-5883 99 26 26 26 NUM cana-5883 99 27 ) ) PUNCT cana-5883 99 28 in in ADP cana-5883 99 29 sequence sequence NOUN cana-5883 99 30 to to PART cana-5883 99 31 find find VERB cana-5883 99 32 the the DET cana-5883 99 33 exact exact ADJ cana-5883 99 34 solution solution NOUN cana-5883 99 35 of of ADP cana-5883 99 36 field field NOUN cana-5883 99 37 equations equation NOUN cana-5883 99 38 following follow VERB cana-5883 99 39 [ [ X cana-5883 99 40 36 36 NUM cana-5883 99 41 ] ] PUNCT cana-5883 99 42 , , PUNCT cana-5883 99 43 we we PRON cana-5883 99 44 assume assume VERB cana-5883 99 45 the the DET cana-5883 99 46 quadratic quadratic ADJ cana-5883 99 47 deceleration deceleration NOUN cana-5883 99 48 parameter parameter NOUN cana-5883 99 49 q q PROPN cana-5883 99 50 which which PRON cana-5883 99 51 is be AUX cana-5883 99 52 given give VERB cana-5883 99 53 by by ADP cana-5883 99 54 , , PUNCT cana-5883 99 55 q q NOUN cana-5883 99 56 = = SYM cana-5883 99 57 βˆ’π‘Ž βˆ’π‘Ž PROPN cana-5883 99 58 οΏ½ οΏ½ PROPN cana-5883 99 59 ̈ ̈ SYM cana-5883 99 60 οΏ½ οΏ½ PROPN cana-5883 99 61 οΏ½ οΏ½ PROPN cana-5883 99 62 Μ‡ Μ‡ PROPN cana-5883 99 63 οΏ½ οΏ½ PROPN cana-5883 99 64 2 2 NUM cana-5883 99 65 = = SYM cana-5883 99 66 3𝑑2 3𝑑2 NUM cana-5883 99 67 - - PUNCT cana-5883 99 68 12𝛽𝑑 12𝛽𝑑 NOUN cana-5883 99 69 + + CCONJ cana-5883 99 70 ( ( PUNCT cana-5883 99 71 8 8 NUM cana-5883 99 72 𝛽2 𝛽2 NOUN cana-5883 99 73 βˆ’ βˆ’ PROPN cana-5883 99 74 1 1 NUM cana-5883 99 75 ) ) PUNCT cana-5883 99 76 ( ( PUNCT cana-5883 99 77 27 27 NUM cana-5883 99 78 ) ) PUNCT cana-5883 99 79 where where SCONJ cana-5883 99 80 𝛽 𝛽 NOUN cana-5883 99 81 is be AUX cana-5883 99 82 positive positive ADJ cana-5883 99 83 constant constant ADJ cana-5883 99 84 . . PUNCT cana-5883 100 1 at at ADP cana-5883 100 2 t=0 t=0 PROPN cana-5883 100 3 , , PUNCT cana-5883 100 4 q q X cana-5883 100 5 = = SYM cana-5883 100 6 ( ( PUNCT cana-5883 100 7 8 8 NUM cana-5883 100 8 𝛽2 𝛽2 PROPN cana-5883 100 9 βˆ’ βˆ’ PROPN cana-5883 100 10 1),which 1),which NUM cana-5883 100 11 is be AUX cana-5883 100 12 always always ADV cana-5883 100 13 positive positive ADJ cana-5883 100 14 for for ADP cana-5883 100 15 all all DET cana-5883 100 16 𝛽 𝛽 NOUN cana-5883 100 17 > > X cana-5883 100 18 0 0 NUM cana-5883 101 1 i.e. i.e. X cana-5883 101 2 given give VERB cana-5883 101 3 form form NOUN cana-5883 101 4 of of ADP cana-5883 101 5 the the DET cana-5883 101 6 deceleration deceleration NOUN cana-5883 101 7 parameter parameter NOUN cana-5883 101 8 in in ADP cana-5883 101 9 ( ( PUNCT cana-5883 101 10 27 27 NUM cana-5883 101 11 ) ) PUNCT cana-5883 101 12 concludes conclude VERB cana-5883 101 13 the the DET cana-5883 101 14 constant constant ADJ cana-5883 101 15 form form NOUN cana-5883 101 16 of of ADP cana-5883 101 17 deceleration deceleration NOUN cana-5883 101 18 parameter parameter NOUN cana-5883 101 19 which which PRON cana-5883 101 20 is be AUX cana-5883 101 21 discussed discuss VERB cana-5883 101 22 by by ADP cana-5883 101 23 [ [ X cana-5883 101 24 41,42 41,42 PROPN cana-5883 101 25 ] ] PUNCT cana-5883 101 26 . . PUNCT cana-5883 102 1 remoter remoter NOUN cana-5883 102 2 this this PRON cana-5883 102 3 was be AUX cana-5883 102 4 extended extend VERB cana-5883 102 5 in in ADP cana-5883 102 6 the the DET cana-5883 102 7 quadratic quadratic ADJ cana-5883 102 8 form form NOUN cana-5883 102 9 of of ADP cana-5883 102 10 time time NOUN cana-5883 102 11 . . PUNCT cana-5883 103 1 at at ADP cana-5883 103 2 the the DET cana-5883 103 3 cyclic cyclic ADJ cana-5883 103 4 term term NOUN cana-5883 103 5 , , PUNCT cana-5883 103 6 this this DET cana-5883 103 7 model model NOUN cana-5883 103 8 starts start VERB cana-5883 103 9 with with ADP cana-5883 103 10 the the DET cana-5883 103 11 big big ADJ cana-5883 103 12 - - PUNCT cana-5883 103 13 bang bang NOUN cana-5883 103 14 singularity singularity NOUN cana-5883 103 15 and and CCONJ cana-5883 103 16 late late ADJ cana-5883 103 17 time time NOUN cana-5883 103 18 in in ADP cana-5883 103 19 a a DET cana-5883 103 20 big big ADJ cana-5883 103 21 rip rip NOUN cana-5883 103 22 . . PUNCT cana-5883 104 1 the the DET cana-5883 104 2 equation equation NOUN cana-5883 104 3 for for ADP cana-5883 104 4 the the DET cana-5883 104 5 deceleration deceleration NOUN cana-5883 104 6 parameter parameter NOUN cana-5883 104 7 is be AUX cana-5883 104 8 given give VERB cana-5883 104 9 by by ADP cana-5883 104 10 , , PUNCT cana-5883 104 11 q q NOUN cana-5883 104 12 = = SYM cana-5883 104 13 βˆ’π‘Ž βˆ’π‘Ž PROPN cana-5883 104 14 οΏ½ οΏ½ PROPN cana-5883 104 15 ̈ ̈ SYM cana-5883 104 16 οΏ½ οΏ½ PROPN cana-5883 104 17 οΏ½ οΏ½ PROPN cana-5883 104 18 Μ‡ Μ‡ PROPN cana-5883 104 19 οΏ½ οΏ½ PROPN cana-5883 104 20 2 2 NUM cana-5883 104 21 = = SYM cana-5883 104 22 βˆ’ βˆ’ PROPN cana-5883 104 23 οΏ½ οΏ½ PROPN cana-5883 104 24 Μ‡ Μ‡ PROPN cana-5883 104 25 οΏ½ οΏ½ PROPN cana-5883 104 26 𝐻2 𝐻2 PROPN cana-5883 104 27 βˆ’ βˆ’ PROPN cana-5883 104 28 1 1 NUM cana-5883 104 29 ( ( PUNCT cana-5883 104 30 28 28 NUM cana-5883 104 31 ) ) PUNCT cana-5883 104 32 with with ADP cana-5883 104 33 the the DET cana-5883 104 34 help help NOUN cana-5883 104 35 of of ADP cana-5883 104 36 equation equation NOUN cana-5883 104 37 ( ( PUNCT cana-5883 104 38 27 27 NUM cana-5883 104 39 ) ) PUNCT cana-5883 104 40 and and CCONJ cana-5883 104 41 ( ( PUNCT cana-5883 104 42 28 28 NUM cana-5883 104 43 ) ) PUNCT cana-5883 104 44 hubble hubble ADJ cana-5883 104 45 parameter parameter NOUN cana-5883 104 46 can can AUX cana-5883 104 47 be be AUX cana-5883 104 48 found find VERB cana-5883 104 49 as as ADP cana-5883 104 50 , , PUNCT cana-5883 104 51 h= h= NOUN cana-5883 104 52 1 1 NUM cana-5883 104 53 𝑑(π‘‘βˆ’2𝛽)(π‘‘βˆ’4𝛽 𝑑(π‘‘βˆ’2𝛽)(π‘‘βˆ’4𝛽 NOUN cana-5883 104 54 ) ) PUNCT cana-5883 104 55 ( ( PUNCT cana-5883 104 56 29 29 NUM cana-5883 104 57 ) ) PUNCT cana-5883 104 58 communications communication NOUN cana-5883 104 59 on on ADP cana-5883 104 60 applied apply VERB cana-5883 104 61 nonlinear nonlinear ADJ cana-5883 104 62 analysis analysis NOUN cana-5883 104 63 issn issn NOUN cana-5883 104 64 : : PUNCT cana-5883 104 65 1074 1074 NUM cana-5883 104 66 - - PUNCT cana-5883 104 67 133x 133x NUM cana-5883 104 68 vol vol NOUN cana-5883 104 69 32 32 NUM cana-5883 104 70 no no NOUN cana-5883 104 71 . . PUNCT cana-5883 105 1 2s 2s NUM cana-5883 105 2 ( ( PUNCT cana-5883 105 3 2025 2025 NUM cana-5883 105 4 ) ) PUNCT cana-5883 105 5 610 610 NUM cana-5883 105 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 105 7 we we PRON cana-5883 105 8 can can AUX cana-5883 105 9 see see VERB cana-5883 105 10 from from ADP cana-5883 105 11 equation equation NOUN cana-5883 105 12 ( ( PUNCT cana-5883 105 13 29 29 NUM cana-5883 105 14 ) ) PUNCT cana-5883 105 15 , , PUNCT cana-5883 105 16 that that SCONJ cana-5883 105 17 the the DET cana-5883 105 18 hubble hubble ADJ cana-5883 105 19 parameter parameter NOUN cana-5883 105 20 h h PROPN cana-5883 105 21 is be AUX cana-5883 105 22 always always ADV cana-5883 105 23 positive positive ADJ cana-5883 105 24 in in ADP cana-5883 105 25 the the DET cana-5883 105 26 range range NOUN cana-5883 105 27 0 0 NUM cana-5883 105 28 ≀ ≀ NUM cana-5883 105 29 𝑑 𝑑 PROPN cana-5883 105 30 ≀ ≀ NOUN cana-5883 105 31 4𝛽. 4𝛽. NOUN cana-5883 106 1 also also ADV cana-5883 106 2 we we PRON cana-5883 106 3 can can AUX cana-5883 106 4 observe observe VERB cana-5883 106 5 that that SCONJ cana-5883 106 6 the the DET cana-5883 106 7 hubble hubble ADJ cana-5883 106 8 parameter parameter NOUN cana-5883 106 9 diverges diverge VERB cana-5883 106 10 at at ADP cana-5883 106 11 t=0 t=0 PROPN cana-5883 106 12 , , PUNCT cana-5883 106 13 t t NOUN cana-5883 106 14 = = SYM cana-5883 106 15 2𝛽 2𝛽 PROPN cana-5883 106 16 and and CCONJ cana-5883 106 17 t t NOUN cana-5883 107 1 = = NOUN cana-5883 107 2 4𝛽 4𝛽 NOUN cana-5883 107 3 integrating integrating NOUN cana-5883 107 4 equation equation NOUN cana-5883 107 5 ( ( PUNCT cana-5883 107 6 29 29 NUM cana-5883 107 7 ) ) PUNCT cana-5883 107 8 , , PUNCT cana-5883 107 9 we we PRON cana-5883 107 10 obtain obtain VERB cana-5883 107 11 the the DET cana-5883 107 12 scale scale NOUN cana-5883 107 13 factor factor NOUN cana-5883 107 14 as as ADP cana-5883 107 15 , , PUNCT cana-5883 107 16 a a PRON cana-5883 107 17 = = X cana-5883 108 1 [ [ X cana-5883 108 2 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 108 3 ) ) PUNCT cana-5883 108 4 ] ] PUNCT cana-5883 108 5 1 1 NUM cana-5883 108 6 8𝛽2 8𝛽2 NUM cana-5883 108 7 [ [ X cana-5883 108 8 ( ( PUNCT cana-5883 108 9 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 108 10 ) ) PUNCT cana-5883 108 11 ] ] PUNCT cana-5883 108 12 1 1 NUM cana-5883 108 13 4𝛽2 4𝛽2 NUM cana-5883 108 14 ( ( PUNCT cana-5883 108 15 30 30 NUM cana-5883 108 16 ) ) PUNCT cana-5883 108 17 which which PRON cana-5883 108 18 gives give VERB cana-5883 108 19 the the DET cana-5883 108 20 declaration declaration NOUN cana-5883 108 21 of of ADP cana-5883 108 22 the the DET cana-5883 108 23 scale scale NOUN cana-5883 108 24 factor factor NOUN cana-5883 108 25 as as ADP cana-5883 108 26 function function NOUN cana-5883 108 27 of of ADP cana-5883 108 28 cosmic cosmic ADJ cana-5883 108 29 time time NOUN cana-5883 108 30 . . PUNCT cana-5883 109 1 it it PRON cana-5883 109 2 is be AUX cana-5883 109 3 remarked remark VERB cana-5883 109 4 that that SCONJ cana-5883 109 5 the the DET cana-5883 109 6 scale scale NOUN cana-5883 109 7 factor factor NOUN cana-5883 109 8 a= a= NOUN cana-5883 109 9 0 0 PUNCT cana-5883 109 10 for for SCONJ cana-5883 109 11 t=0 t=0 PROPN cana-5883 109 12 and and CCONJ cana-5883 109 13 at at ADP cana-5883 109 14 t t NOUN cana-5883 109 15 = = SYM cana-5883 109 16 4𝛽 4𝛽 NUM cana-5883 109 17 and and CCONJ cana-5883 109 18 scale scale NOUN cana-5883 109 19 factor factor NOUN cana-5883 109 20 diverges diverge VERB cana-5883 109 21 at at ADP cana-5883 109 22 t= t= ADJ cana-5883 109 23 2𝛽 2𝛽 NOUN cana-5883 109 24 , , PUNCT cana-5883 109 25 which which PRON cana-5883 109 26 manifest manifest VERB cana-5883 109 27 that that SCONJ cana-5883 109 28 the the DET cana-5883 109 29 universe universe NOUN cana-5883 109 30 starts start VERB cana-5883 109 31 with with ADP cana-5883 109 32 big big ADJ cana-5883 109 33 - - PUNCT cana-5883 109 34 bang bang NOUN cana-5883 109 35 at at ADP cana-5883 109 36 t=0 t=0 PROPN cana-5883 109 37 and and CCONJ cana-5883 109 38 ends end VERB cana-5883 109 39 with with ADP cana-5883 109 40 big big ADJ cana-5883 109 41 crunch crunch NOUN cana-5883 109 42 at at ADP cana-5883 109 43 t=2 t=2 PROPN cana-5883 109 44 𝛽. 𝛽. NOUN cana-5883 109 45 from from ADP cana-5883 109 46 equations equation NOUN cana-5883 109 47 ( ( PUNCT cana-5883 109 48 19)-(21 19)-(21 ADV cana-5883 109 49 ) ) PUNCT cana-5883 109 50 together together ADV cana-5883 109 51 with with ADP cana-5883 109 52 equation equation NOUN cana-5883 109 53 ( ( PUNCT cana-5883 109 54 31 31 NUM cana-5883 109 55 ) ) PUNCT cana-5883 109 56 & & CCONJ cana-5883 109 57 ( ( PUNCT cana-5883 109 58 32 32 NUM cana-5883 109 59 ) ) PUNCT cana-5883 109 60 , , PUNCT cana-5883 109 61 we we PRON cana-5883 109 62 get get VERB cana-5883 109 63 – – PUNCT cana-5883 109 64 π‘Ž1Μ‡ π‘Ž1Μ‡ VERB cana-5883 109 65 π‘Ž1 π‘Ž1 NOUN cana-5883 109 66 = = SYM cana-5883 109 67 1 1 NUM cana-5883 109 68 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ NOUN cana-5883 109 69 ) ) PUNCT cana-5883 109 70 ( ( PUNCT cana-5883 109 71 31 31 NUM cana-5883 109 72 ) ) PUNCT cana-5883 109 73 π‘Ž2Μ‡ π‘Ž2Μ‡ NOUN cana-5883 109 74 π‘Ž2 π‘Ž2 NOUN cana-5883 109 75 = = NOUN cana-5883 109 76 1 1 NUM cana-5883 109 77 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ NOUN cana-5883 109 78 ) ) PUNCT cana-5883 109 79 – – PUNCT cana-5883 110 1 [ [ X cana-5883 110 2 ( ( PUNCT cana-5883 110 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 110 4 ) ) PUNCT cana-5883 110 5 ] ] PUNCT cana-5883 110 6 3 3 NUM cana-5883 110 7 4𝛽2 4𝛽2 NUM cana-5883 110 8 π‘˜ π‘˜ X cana-5883 111 1 [ [ X cana-5883 111 2 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 111 3 ) ) PUNCT cana-5883 111 4 ] ] PUNCT cana-5883 111 5 3 3 NUM cana-5883 111 6 8𝛽2 8𝛽2 NUM cana-5883 111 7 ( ( PUNCT cana-5883 111 8 32 32 NUM cana-5883 111 9 ) ) PUNCT cana-5883 111 10 π‘Ž3Μ‡ π‘Ž3Μ‡ NOUN cana-5883 111 11 π‘Ž3 π‘Ž3 NOUN cana-5883 111 12 = = SYM cana-5883 111 13 1 1 NUM cana-5883 111 14 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ 𝑑(2π›½βˆ’π‘‘)(4π›½βˆ’π‘‘ NOUN cana-5883 111 15 ) ) PUNCT cana-5883 111 16 + + CCONJ cana-5883 112 1 [ [ X cana-5883 112 2 ( ( PUNCT cana-5883 112 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 112 4 ) ) PUNCT cana-5883 112 5 ] ] PUNCT cana-5883 113 1 3 3 NUM cana-5883 113 2 4𝛽2 4𝛽2 NUM cana-5883 113 3 π‘˜ π‘˜ X cana-5883 114 1 [ [ X cana-5883 114 2 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 114 3 ) ) PUNCT cana-5883 114 4 ] ] PUNCT cana-5883 114 5 3 3 NUM cana-5883 114 6 8𝛽2 8𝛽2 NUM cana-5883 114 7 ( ( PUNCT cana-5883 114 8 33 33 NUM cana-5883 114 9 ) ) PUNCT cana-5883 114 10 which which PRON cana-5883 114 11 gives give VERB cana-5883 114 12 , , PUNCT cana-5883 114 13 π‘Ž1 π‘Ž1 NOUN cana-5883 114 14 = = PRON cana-5883 114 15 [ [ PUNCT cana-5883 114 16 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 114 17 ) ) PUNCT cana-5883 114 18 ( ( PUNCT cana-5883 114 19 2π›½βˆ’π‘‘)2 2π›½βˆ’π‘‘)2 NUM cana-5883 114 20 ] ] SYM cana-5883 114 21 1 1 NUM cana-5883 114 22 8𝛽2 8𝛽2 NUM cana-5883 114 23 ( ( PUNCT cana-5883 114 24 34 34 NUM cana-5883 114 25 ) ) PUNCT cana-5883 114 26 π‘Ž2 π‘Ž2 NOUN cana-5883 114 27 = = SYM cana-5883 114 28 [ [ PUNCT cana-5883 114 29 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 114 30 ) ) PUNCT cana-5883 114 31 ( ( PUNCT cana-5883 114 32 2π›½βˆ’π‘‘)2 2π›½βˆ’π‘‘)2 NUM cana-5883 114 33 ] ] SYM cana-5883 114 34 1 1 NUM cana-5883 114 35 8𝛽2 8𝛽2 NUM cana-5883 114 36 βˆ’ βˆ’ NOUN cana-5883 114 37 ∫ ∫ PROPN cana-5883 115 1 [ [ X cana-5883 115 2 ( ( PUNCT cana-5883 115 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 115 4 ) ) PUNCT cana-5883 115 5 ] ] PUNCT cana-5883 116 1 3 3 NUM cana-5883 116 2 4𝛽2 4𝛽2 NUM cana-5883 116 3 π‘˜ π‘˜ X cana-5883 117 1 [ [ X cana-5883 117 2 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 117 3 ) ) PUNCT cana-5883 117 4 ] ] PUNCT cana-5883 117 5 3 3 NUM cana-5883 117 6 8𝛽2 8𝛽2 NUM cana-5883 117 7 dt dt NOUN cana-5883 117 8 ( ( PUNCT cana-5883 117 9 35 35 NUM cana-5883 117 10 ) ) PUNCT cana-5883 117 11 π‘Ž3 π‘Ž3 NOUN cana-5883 117 12 = = PUNCT cana-5883 117 13 [ [ PUNCT cana-5883 117 14 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 117 15 ) ) PUNCT cana-5883 117 16 ( ( PUNCT cana-5883 117 17 2π›½βˆ’π‘‘)2 2π›½βˆ’π‘‘)2 NUM cana-5883 117 18 ] ] SYM cana-5883 117 19 1 1 NUM cana-5883 117 20 8𝛽2 8𝛽2 NUM cana-5883 117 21 + + NUM cana-5883 117 22 ∫ ∫ PROPN cana-5883 118 1 [ [ X cana-5883 118 2 ( ( PUNCT cana-5883 118 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 118 4 ) ) PUNCT cana-5883 118 5 ] ] PUNCT cana-5883 119 1 3 3 NUM cana-5883 119 2 4𝛽2 4𝛽2 NUM cana-5883 119 3 π‘˜ π‘˜ X cana-5883 120 1 [ [ X cana-5883 120 2 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 120 3 ) ) PUNCT cana-5883 120 4 ] ] PUNCT cana-5883 120 5 3 3 NUM cana-5883 120 6 8𝛽2 8𝛽2 NUM cana-5883 120 7 dt dt NOUN cana-5883 120 8 ( ( PUNCT cana-5883 120 9 36 36 NUM cana-5883 120 10 ) ) PUNCT cana-5883 120 11 relation relation NOUN cana-5883 120 12 between between ADP cana-5883 120 13 scale scale NOUN cana-5883 120 14 factor factor NOUN cana-5883 120 15 and and CCONJ cana-5883 120 16 redshift redshift NOUN cana-5883 120 17 is be AUX cana-5883 120 18 given give VERB cana-5883 120 19 as as ADP cana-5883 120 20 , , PUNCT cana-5883 120 21 π‘Ž π‘Ž NOUN cana-5883 120 22 π‘Ž0 π‘Ž0 NOUN cana-5883 120 23 = = SYM cana-5883 120 24 1 1 NUM cana-5883 120 25 1+𝑧 1+𝑧 NUM cana-5883 120 26 ( ( PUNCT cana-5883 120 27 37 37 NUM cana-5883 120 28 ) ) PUNCT cana-5883 120 29 from from ADP cana-5883 120 30 equation equation NOUN cana-5883 120 31 ( ( PUNCT cana-5883 120 32 30 30 NUM cana-5883 120 33 ) ) PUNCT cana-5883 120 34 and and CCONJ cana-5883 120 35 ( ( PUNCT cana-5883 120 36 37 37 NUM cana-5883 120 37 ) ) PUNCT cana-5883 120 38 we we PRON cana-5883 120 39 have have VERB cana-5883 120 40 , , PUNCT cana-5883 120 41 communications communication NOUN cana-5883 120 42 on on ADP cana-5883 120 43 applied apply VERB cana-5883 120 44 nonlinear nonlinear ADJ cana-5883 120 45 analysis analysis NOUN cana-5883 120 46 issn issn NOUN cana-5883 120 47 : : PUNCT cana-5883 120 48 1074 1074 NUM cana-5883 120 49 - - PUNCT cana-5883 120 50 133x 133x NUM cana-5883 120 51 vol vol NOUN cana-5883 120 52 32 32 NUM cana-5883 120 53 no no NOUN cana-5883 120 54 . . PUNCT cana-5883 121 1 2s 2s NUM cana-5883 121 2 ( ( PUNCT cana-5883 121 3 2025 2025 NUM cana-5883 121 4 ) ) PUNCT cana-5883 121 5 611 611 NUM cana-5883 121 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 121 7 [ [ PUNCT cana-5883 121 8 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 121 9 ) ) PUNCT cana-5883 121 10 ( ( PUNCT cana-5883 121 11 2π›½βˆ’π‘‘)2 2π›½βˆ’π‘‘)2 NUM cana-5883 121 12 ] ] SYM cana-5883 121 13 1 1 NUM cana-5883 121 14 8𝛽2 8𝛽2 NUM cana-5883 121 15 = = SYM cana-5883 121 16 1 1 NUM cana-5883 121 17 1+𝑧 1+𝑧 NUM cana-5883 121 18 ( ( PUNCT cana-5883 121 19 38 38 NUM cana-5883 121 20 ) ) PUNCT cana-5883 121 21 to to PART cana-5883 121 22 find find VERB cana-5883 121 23 the the DET cana-5883 121 24 value value NOUN cana-5883 121 25 of of ADP cana-5883 121 26 time time NOUN cana-5883 121 27 in in ADP cana-5883 121 28 the the DET cana-5883 121 29 term term NOUN cana-5883 121 30 of of ADP cana-5883 121 31 red red ADJ cana-5883 121 32 shift shift NOUN cana-5883 121 33 , , PUNCT cana-5883 121 34 we we PRON cana-5883 121 35 have have AUX cana-5883 121 36 taken take VERB cana-5883 121 37 the the DET cana-5883 121 38 choice choice NOUN cana-5883 121 39 of of ADP cana-5883 121 40 𝛽 𝛽 NOUN cana-5883 121 41 . . PUNCT cana-5883 122 1 so so ADV cana-5883 122 2 , , PUNCT cana-5883 122 3 we we PRON cana-5883 122 4 assume assume VERB cana-5883 122 5 , , PUNCT cana-5883 122 6 1 1 NUM cana-5883 122 7 4𝛽2 4𝛽2 NUM cana-5883 122 8 = = SYM cana-5883 123 1 1 1 NUM cana-5883 123 2 ⟹ ⟹ NUM cana-5883 123 3 𝛽 𝛽 NOUN cana-5883 123 4 = = SYM cana-5883 123 5 0.5 0.5 NUM cana-5883 123 6 , , PUNCT cana-5883 123 7 which which PRON cana-5883 123 8 can can AUX cana-5883 123 9 help help VERB cana-5883 123 10 to to PART cana-5883 123 11 express express VERB cana-5883 123 12 t t NOUN cana-5883 123 13 as as ADP cana-5883 123 14 , , PUNCT cana-5883 123 15 t t PROPN cana-5883 123 16 = = SYM cana-5883 123 17 1Β± 1Β± NUM cana-5883 123 18 1+𝑍 1+𝑍 NOUN cana-5883 123 19 βˆšπ‘(𝑍+2)+2 βˆšπ‘(𝑍+2)+2 NOUN cana-5883 123 20 ( ( PUNCT cana-5883 123 21 39 39 NUM cana-5883 123 22 ) ) PUNCT cana-5883 123 23 the the DET cana-5883 123 24 hubble hubble ADJ cana-5883 123 25 parameter parameter NOUN cana-5883 123 26 in in ADP cana-5883 123 27 the the DET cana-5883 123 28 terms term NOUN cana-5883 123 29 of of ADP cana-5883 123 30 redshift redshift NOUN cana-5883 123 31 ( ( PUNCT cana-5883 123 32 z z NOUN cana-5883 123 33 ) ) PUNCT cana-5883 123 34 conceivably conceivably ADV cana-5883 123 35 expressed express VERB cana-5883 123 36 as as ADP cana-5883 123 37 , , PUNCT cana-5883 123 38 h h NOUN cana-5883 123 39 = = NOUN cana-5883 123 40 ho ho PROPN cana-5883 124 1 [ [ X cana-5883 124 2 1Β± 1Β± NUM cana-5883 124 3 1+𝑧 1+𝑧 NUM cana-5883 124 4 βˆšπ‘§(𝑧+2)+2 βˆšπ‘§(𝑧+2)+2 NOUN cana-5883 124 5 ] ] PUNCT cana-5883 124 6 3 3 NUM cana-5883 124 7 βˆ’6𝛽[1Β± βˆ’6𝛽[1Β± SYM cana-5883 124 8 1+𝑧 1+𝑧 NUM cana-5883 124 9 βˆšπ‘§(𝑧+2)+2 βˆšπ‘§(𝑧+2)+2 NOUN cana-5883 124 10 ] ] PUNCT cana-5883 124 11 2 2 NUM cana-5883 124 12 +8 +8 PROPN cana-5883 124 13 𝛽2[1Β± 𝛽2[1Β± PROPN cana-5883 124 14 1+𝑧 1+𝑧 NUM cana-5883 124 15 βˆšπ‘§(𝑧+2)+2 βˆšπ‘§(𝑧+2)+2 NOUN cana-5883 124 16 ] ] PUNCT cana-5883 124 17 concerning concern VERB cana-5883 124 18 red red ADJ cana-5883 124 19 shift shift NOUN cana-5883 124 20 , , PUNCT cana-5883 124 21 deceleration deceleration NOUN cana-5883 124 22 parameter parameter NOUN cana-5883 124 23 can can AUX cana-5883 124 24 be be AUX cana-5883 124 25 stated state VERB cana-5883 124 26 as as ADP cana-5883 124 27 , , PUNCT cana-5883 124 28 q q X cana-5883 124 29 ( ( PUNCT cana-5883 124 30 z z NOUN cana-5883 124 31 ) ) PUNCT cana-5883 124 32 = = PUNCT cana-5883 125 1 𝑧2 𝑧2 PROPN cana-5883 125 2 + + PROPN cana-5883 125 3 2π‘§βˆ’1 2π‘§βˆ’1 NUM cana-5883 125 4 𝑧2 𝑧2 NOUN cana-5883 125 5 + + NOUN cana-5883 125 6 2𝑧+2 2𝑧+2 PROPN cana-5883 125 7 ( ( PUNCT cana-5883 125 8 40 40 NUM cana-5883 125 9 ) ) PUNCT cana-5883 125 10 as as ADP cana-5883 125 11 the the DET cana-5883 125 12 consequence consequence NOUN cana-5883 125 13 ( ( PUNCT cana-5883 125 14 26 26 NUM cana-5883 125 15 ) ) PUNCT cana-5883 125 16 , , PUNCT cana-5883 125 17 ( ( PUNCT cana-5883 125 18 27 27 NUM cana-5883 125 19 ) ) PUNCT cana-5883 125 20 , , PUNCT cana-5883 125 21 ( ( PUNCT cana-5883 125 22 28 28 NUM cana-5883 125 23 ) ) PUNCT cana-5883 125 24 , , PUNCT cana-5883 125 25 ( ( PUNCT cana-5883 125 26 31 31 NUM cana-5883 125 27 ) ) PUNCT cana-5883 125 28 & & CCONJ cana-5883 125 29 ( ( PUNCT cana-5883 125 30 32 32 NUM cana-5883 125 31 ) ) PUNCT cana-5883 125 32 , , PUNCT cana-5883 125 33 the the DET cana-5883 125 34 energy energy NOUN cana-5883 125 35 density density NOUN cana-5883 125 36 , , PUNCT cana-5883 125 37 pressure pressure NOUN cana-5883 125 38 and and CCONJ cana-5883 125 39 cosmological cosmological ADJ cana-5883 125 40 term term NOUN cana-5883 125 41 of of ADP cana-5883 125 42 model model NOUN cana-5883 125 43 are be AUX cana-5883 125 44 express express ADJ cana-5883 125 45 as as ADP cana-5883 125 46 , , PUNCT cana-5883 125 47 𝜌 𝜌 X cana-5883 125 48 = = SYM cana-5883 125 49 2πœ†2 2πœ†2 NUM cana-5883 125 50 [ [ X cana-5883 125 51 ( ( PUNCT cana-5883 125 52 8Ο€+3Ξ»)2βˆ’Ξ»2 8Ο€+3Ξ»)2βˆ’Ξ»2 NUM cana-5883 125 53 [ [ PUNCT cana-5883 125 54 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ NUM cana-5883 125 55 + + SYM cana-5883 125 56 8 8 NUM cana-5883 125 57 πœ†π›½2βˆ’(24Ο€+3Ξ» πœ†π›½2βˆ’(24Ο€+3Ξ» NOUN cana-5883 125 58 ) ) PUNCT cana-5883 125 59 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 126 1 + + CCONJ cana-5883 126 2 ( ( PUNCT cana-5883 126 3 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 126 4 ) ) PUNCT cana-5883 126 5 k2 k2 PROPN cana-5883 127 1 [ [ X cana-5883 127 2 ( ( PUNCT cana-5883 127 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 127 4 ) ) PUNCT cana-5883 127 5 ] ] PUNCT cana-5883 127 6 3 3 NUM cana-5883 127 7 2𝛽2 2𝛽2 NUM cana-5883 127 8 λ𝑑 λ𝑑 VERB cana-5883 127 9 3 3 NUM cana-5883 127 10 4𝛽2(4π›½βˆ’π‘‘ 4𝛽2(4π›½βˆ’π‘‘ NOUN cana-5883 127 11 ) ) PUNCT cana-5883 127 12 ] ] PUNCT cana-5883 127 13 3 3 NUM cana-5883 127 14 4𝛽2 4𝛽2 NUM cana-5883 127 15 + + CCONJ cana-5883 127 16 ( ( PUNCT cana-5883 127 17 24Ο€+4Ξ» 24Ο€+4Ξ» NUM cana-5883 127 18 ) ) PUNCT cana-5883 128 1 [ [ X cana-5883 128 2 ( ( PUNCT cana-5883 128 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 128 4 ) ) PUNCT cana-5883 128 5 ] ] PUNCT cana-5883 128 6 1 1 NUM cana-5883 128 7 2𝛽2 2𝛽2 NUM cana-5883 128 8 Ξ» Ξ» NOUN cana-5883 128 9 𝑑 𝑑 NOUN cana-5883 128 10 1 1 NUM cana-5883 128 11 4𝛽2(4π›½βˆ’π‘‘ 4𝛽2(4π›½βˆ’π‘‘ NOUN cana-5883 128 12 ) ) PUNCT cana-5883 128 13 ] ] PUNCT cana-5883 128 14 1 1 NUM cana-5883 128 15 4𝛽2 4𝛽2 NUM cana-5883 128 16 ] ] PUNCT cana-5883 128 17 ( ( PUNCT cana-5883 128 18 41 41 NUM cana-5883 128 19 ) ) PUNCT cana-5883 128 20 p p NOUN cana-5883 128 21 = = X cana-5883 128 22 2πœ†2 2πœ†2 NUM cana-5883 129 1 [ [ X cana-5883 129 2 ( ( PUNCT cana-5883 129 3 8Ο€+3Ξ»)2βˆ’Ξ»2 8Ο€+3Ξ»)2βˆ’Ξ»2 NUM cana-5883 129 4 ] ] X cana-5883 129 5 [ [ PUNCT cana-5883 129 6 ( ( PUNCT cana-5883 129 7 16Ο€+3Ξ» 16Ο€+3Ξ» NUM cana-5883 129 8 ) ) PUNCT cana-5883 129 9 3𝑑2βˆ’12𝛽𝑑+ 3𝑑2βˆ’12𝛽𝑑+ NOUN cana-5883 129 10 24 24 NUM cana-5883 129 11 𝛽2(8Ο€+Ξ» 𝛽2(8Ο€+Ξ» PROPN cana-5883 129 12 ) ) PUNCT cana-5883 129 13 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 130 1 + + CCONJ cana-5883 130 2 ( ( PUNCT cana-5883 130 3 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 130 4 ) ) PUNCT cana-5883 130 5 k2 k2 PROPN cana-5883 130 6 [ [ X cana-5883 130 7 ( ( PUNCT cana-5883 130 8 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 130 9 ) ) PUNCT cana-5883 130 10 ] ] PUNCT cana-5883 130 11 3 3 NUM cana-5883 130 12 2𝛽2 2𝛽2 NUM cana-5883 130 13 λ𝑑 λ𝑑 VERB cana-5883 130 14 3 3 NUM cana-5883 130 15 4𝛽2(4π›½βˆ’π‘‘ 4𝛽2(4π›½βˆ’π‘‘ NOUN cana-5883 130 16 ) ) PUNCT cana-5883 130 17 3 3 NUM cana-5883 130 18 4𝛽2 4𝛽2 NUM cana-5883 130 19 βˆ’ βˆ’ PROPN cana-5883 131 1 ( ( PUNCT cana-5883 131 2 8πλ 8πλ NOUN cana-5883 131 3 ) ) PUNCT cana-5883 132 1 [ [ X cana-5883 132 2 ( ( PUNCT cana-5883 132 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 132 4 ) ) PUNCT cana-5883 132 5 ] ] PUNCT cana-5883 132 6 1 1 NUM cana-5883 132 7 2𝛽2 2𝛽2 NUM cana-5883 132 8 𝑑 𝑑 NOUN cana-5883 132 9 1 1 NUM cana-5883 132 10 4𝛽2(4π›½βˆ’π‘‘ 4𝛽2(4π›½βˆ’π‘‘ NOUN cana-5883 132 11 ) ) PUNCT cana-5883 132 12 1 1 NUM cana-5883 132 13 4𝛽2 4𝛽2 NOUN cana-5883 132 14 ] ] PUNCT cana-5883 132 15 ( ( PUNCT cana-5883 132 16 42 42 X cana-5883 132 17 ) ) PUNCT cana-5883 132 18 ʌ ʌ X cana-5883 132 19 = = SYM cana-5883 132 20 Ξ»2(8Ο€+Ξ» Ξ»2(8Ο€+Ξ» PROPN cana-5883 132 21 ) ) PUNCT cana-5883 133 1 [ [ X cana-5883 133 2 ( ( PUNCT cana-5883 133 3 8Ο€+3Ξ»)2 8Ο€+3Ξ»)2 NUM cana-5883 133 4 βˆ’Ξ»2 βˆ’Ξ»2 NOUN cana-5883 133 5 ] ] X cana-5883 133 6 [ [ PUNCT cana-5883 133 7 ( ( PUNCT cana-5883 133 8 6𝑑2βˆ’24𝛽𝑑 6𝑑2βˆ’24𝛽𝑑 NUM cana-5883 133 9 + + NOUN cana-5883 133 10 16𝛽2 16𝛽2 NUM cana-5883 133 11 + + NOUN cana-5883 133 12 3 3 NUM cana-5883 133 13 ) ) PUNCT cana-5883 133 14 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 133 15 + + NUM cana-5883 133 16 4[(2π›½βˆ’π‘‘ 4[(2π›½βˆ’π‘‘ NOUN cana-5883 133 17 ) ) PUNCT cana-5883 133 18 ] ] PUNCT cana-5883 133 19 1 1 NUM cana-5883 133 20 2𝛽2 2𝛽2 NUM cana-5883 133 21 𝑑(4π›½βˆ’π‘‘ 𝑑(4π›½βˆ’π‘‘ NOUN cana-5883 133 22 ) ) PUNCT cana-5883 133 23 ] ] PUNCT cana-5883 133 24 1 1 NUM cana-5883 133 25 4𝛽2 4𝛽2 NUM cana-5883 133 26 ] ] PUNCT cana-5883 133 27 ( ( PUNCT cana-5883 133 28 43 43 NUM cana-5883 133 29 ) ) PUNCT cana-5883 133 30 the the DET cana-5883 133 31 equalization equalization NOUN cana-5883 133 32 of of ADP cana-5883 133 33 state state NOUN cana-5883 133 34 parameter parameter NOUN cana-5883 133 35 ( ( PUNCT cana-5883 133 36 p p NOUN cana-5883 133 37 = = X cana-5883 133 38 πœ”πœŒ)is πœ”πœŒ)is PUNCT cana-5883 133 39 given give VERB cana-5883 133 40 by by ADP cana-5883 133 41 , , PUNCT cana-5883 133 42 communications communication NOUN cana-5883 133 43 on on ADP cana-5883 133 44 applied apply VERB cana-5883 133 45 nonlinear nonlinear ADJ cana-5883 133 46 analysis analysis NOUN cana-5883 133 47 issn issn NOUN cana-5883 133 48 : : PUNCT cana-5883 133 49 1074 1074 NUM cana-5883 133 50 - - PUNCT cana-5883 133 51 133x 133x NUM cana-5883 133 52 vol vol NOUN cana-5883 133 53 32 32 NUM cana-5883 133 54 no no NOUN cana-5883 133 55 . . PUNCT cana-5883 134 1 2s 2s NUM cana-5883 134 2 ( ( PUNCT cana-5883 134 3 2025 2025 NUM cana-5883 134 4 ) ) PUNCT cana-5883 134 5 612 612 NUM cana-5883 134 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 134 7 πœ”= πœ”= NOUN cana-5883 134 8 [ [ PUNCT cana-5883 134 9 ( ( PUNCT cana-5883 134 10 16Ο€+3Ξ» 16Ο€+3Ξ» NUM cana-5883 134 11 ) ) PUNCT cana-5883 134 12 3𝑑2βˆ’12𝛽𝑑+ 3𝑑2βˆ’12𝛽𝑑+ NOUN cana-5883 134 13 24 24 NUM cana-5883 134 14 𝛽2(8Ο€+Ξ» 𝛽2(8Ο€+Ξ» PROPN cana-5883 134 15 ) ) PUNCT cana-5883 134 16 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 λ𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 135 1 + + CCONJ cana-5883 135 2 ( ( PUNCT cana-5883 135 3 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 135 4 ) ) PUNCT cana-5883 135 5 k2 k2 PROPN cana-5883 135 6 [ [ X cana-5883 135 7 ( ( PUNCT cana-5883 135 8 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 135 9 ) ) PUNCT cana-5883 135 10 ] ] PUNCT cana-5883 135 11 3 3 NUM cana-5883 135 12 2𝛽2 2𝛽2 NUM cana-5883 135 13 λ𝑑 λ𝑑 VERB cana-5883 135 14 3 3 NUM cana-5883 135 15 4𝛽2 4𝛽2 NUM cana-5883 135 16 ( ( PUNCT cana-5883 135 17 4π›½βˆ’π‘‘ 4π›½βˆ’π‘‘ NUM cana-5883 135 18 ) ) PUNCT cana-5883 135 19 3 3 NUM cana-5883 135 20 4𝛽2 4𝛽2 NUM cana-5883 135 21 βˆ’ βˆ’ PROPN cana-5883 135 22 ( ( PUNCT cana-5883 135 23 8πλ 8πλ NOUN cana-5883 135 24 ) ) PUNCT cana-5883 136 1 [ [ X cana-5883 136 2 ( ( PUNCT cana-5883 136 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 136 4 ) ) PUNCT cana-5883 136 5 ] ] PUNCT cana-5883 136 6 1 1 NUM cana-5883 136 7 2𝛽2 2𝛽2 NUM cana-5883 136 8 𝑑 𝑑 VERB cana-5883 136 9 1 1 NUM cana-5883 136 10 4𝛽2 4𝛽2 NUM cana-5883 136 11 ( ( PUNCT cana-5883 136 12 4π›½βˆ’π‘‘ 4π›½βˆ’π‘‘ NOUN cana-5883 136 13 ) ) PUNCT cana-5883 136 14 1 1 NUM cana-5883 136 15 4𝛽2 4𝛽2 NOUN cana-5883 136 16 ] ] PUNCT cana-5883 136 17 [ [ PUNCT cana-5883 136 18 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ NUM cana-5883 136 19 + + SYM cana-5883 136 20 8 8 NUM cana-5883 136 21 πœ†π›½2βˆ’(24Ο€+3Ξ» πœ†π›½2βˆ’(24Ο€+3Ξ» NOUN cana-5883 136 22 ) ) PUNCT cana-5883 136 23 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 137 1 + + CCONJ cana-5883 137 2 ( ( PUNCT cana-5883 137 3 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 137 4 ) ) PUNCT cana-5883 137 5 k2 k2 PROPN cana-5883 138 1 [ [ X cana-5883 138 2 ( ( PUNCT cana-5883 138 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 138 4 ) ) PUNCT cana-5883 138 5 ] ] PUNCT cana-5883 138 6 3 3 NUM cana-5883 138 7 2𝛽2 2𝛽2 NUM cana-5883 138 8 λ𝑑 λ𝑑 VERB cana-5883 138 9 3 3 NUM cana-5883 138 10 4𝛽2 4𝛽2 NUM cana-5883 138 11 ( ( PUNCT cana-5883 138 12 4π›½βˆ’π‘‘ 4π›½βˆ’π‘‘ NOUN cana-5883 138 13 ) ) PUNCT cana-5883 138 14 ] ] PUNCT cana-5883 138 15 3 3 NUM cana-5883 138 16 4𝛽2 4𝛽2 NUM cana-5883 138 17 + + CCONJ cana-5883 138 18 ( ( PUNCT cana-5883 138 19 24Ο€+4Ξ» 24Ο€+4Ξ» NUM cana-5883 138 20 ) ) PUNCT cana-5883 138 21 Ξ»[(2π›½βˆ’π‘‘ Ξ»[(2π›½βˆ’π‘‘ X cana-5883 138 22 ) ) PUNCT cana-5883 138 23 ] ] PUNCT cana-5883 138 24 1 1 NUM cana-5883 138 25 2𝛽2 2𝛽2 NUM cana-5883 138 26 𝑑 𝑑 VERB cana-5883 138 27 1 1 NUM cana-5883 138 28 4𝛽2 4𝛽2 NUM cana-5883 138 29 ( ( PUNCT cana-5883 138 30 4π›½βˆ’π‘‘ 4π›½βˆ’π‘‘ NOUN cana-5883 138 31 ) ) PUNCT cana-5883 138 32 ] ] PUNCT cana-5883 138 33 1 1 NUM cana-5883 138 34 4𝛽2 4𝛽2 NUM cana-5883 138 35 ] ] PUNCT cana-5883 138 36 ( ( PUNCT cana-5883 138 37 44 44 NUM cana-5883 138 38 ) ) PUNCT cana-5883 138 39 identification identification NOUN cana-5883 138 40 of of ADP cana-5883 138 41 restriction restriction NOUN cana-5883 138 42 ( ( PUNCT cana-5883 138 43 πœ” πœ” NOUN cana-5883 138 44 ) ) PUNCT cana-5883 138 45 , , PUNCT cana-5883 138 46 as as SCONJ cana-5883 138 47 regards regard VERB cana-5883 138 48 red red ADJ cana-5883 138 49 shift shift NOUN cana-5883 138 50 as as ADP cana-5883 138 51 , , PUNCT cana-5883 138 52 πœ”(𝑧)= πœ”(𝑧)= PROPN cana-5883 138 53 [ [ PUNCT cana-5883 138 54 ( ( PUNCT cana-5883 138 55 16Ο€ 16Ο€ X cana-5883 138 56 + + CCONJ cana-5883 138 57 3Ξ» 3Ξ» NUM cana-5883 138 58 ) ) PUNCT cana-5883 138 59 3 3 NUM cana-5883 139 1 [ [ SYM cana-5883 139 2 1 1 NUM cana-5883 139 3 Β± Β± NUM cana-5883 139 4 1 1 NUM cana-5883 139 5 + + CCONJ cana-5883 139 6 𝑍 𝑍 PROPN cana-5883 139 7 βˆšπ‘(𝑍 βˆšπ‘(𝑍 NOUN cana-5883 139 8 + + CCONJ cana-5883 139 9 2 2 NUM cana-5883 139 10 ) ) PUNCT cana-5883 139 11 + + CCONJ cana-5883 139 12 2 2 X cana-5883 139 13 ] ] SYM cana-5883 139 14 2 2 NUM cana-5883 139 15 βˆ’ βˆ’ NOUN cana-5883 139 16 12𝛽 12𝛽 NOUN cana-5883 140 1 [ [ X cana-5883 140 2 1 1 NUM cana-5883 140 3 Β± Β± NUM cana-5883 140 4 1 1 NUM cana-5883 140 5 + + CCONJ cana-5883 140 6 𝑍 𝑍 PROPN cana-5883 140 7 βˆšπ‘(𝑍 βˆšπ‘(𝑍 NOUN cana-5883 140 8 + + CCONJ cana-5883 140 9 2 2 NUM cana-5883 140 10 ) ) PUNCT cana-5883 140 11 + + CCONJ cana-5883 140 12 2 2 NUM cana-5883 140 13 ] ] PUNCT cana-5883 140 14 + + CCONJ cana-5883 140 15 24 24 NUM cana-5883 140 16 𝛽2(8Ο€ 𝛽2(8Ο€ NOUN cana-5883 140 17 + + CCONJ cana-5883 140 18 Ξ» Ξ» NOUN cana-5883 140 19 ) ) PUNCT cana-5883 140 20 Ξ» Ξ» PROPN cana-5883 141 1 [ [ X cana-5883 141 2 1 1 NUM cana-5883 141 3 Β± Β± NUM cana-5883 141 4 1 1 NUM cana-5883 141 5 + + CCONJ cana-5883 141 6 𝑧 𝑧 DET cana-5883 141 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 141 8 + + CCONJ cana-5883 141 9 2 2 X cana-5883 141 10 ) ) PUNCT cana-5883 141 11 + + CCONJ cana-5883 141 12 2 2 NUM cana-5883 141 13 ] ] SYM cana-5883 141 14 2 2 NUM cana-5883 141 15 ( ( PUNCT cana-5883 141 16 [ [ X cana-5883 141 17 1 1 NUM cana-5883 141 18 Β± Β± NUM cana-5883 141 19 1 1 NUM cana-5883 141 20 + + CCONJ cana-5883 141 21 𝑧 𝑧 DET cana-5883 141 22 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 141 23 + + CCONJ cana-5883 141 24 2 2 X cana-5883 141 25 ) ) PUNCT cana-5883 141 26 + + CCONJ cana-5883 141 27 2 2 X cana-5883 141 28 ] ] PUNCT cana-5883 141 29 βˆ’ βˆ’ NOUN cana-5883 141 30 2𝛽 2𝛽 NOUN cana-5883 141 31 ) ) PUNCT cana-5883 141 32 2 2 NUM cana-5883 141 33 ( ( PUNCT cana-5883 141 34 [ [ X cana-5883 141 35 1 1 NUM cana-5883 141 36 Β± Β± NUM cana-5883 141 37 1 1 NUM cana-5883 141 38 + + CCONJ cana-5883 141 39 𝑧 𝑧 DET cana-5883 141 40 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 141 41 + + CCONJ cana-5883 141 42 2 2 X cana-5883 141 43 ) ) PUNCT cana-5883 141 44 + + CCONJ cana-5883 141 45 2 2 X cana-5883 141 46 ] ] PUNCT cana-5883 141 47 βˆ’ βˆ’ NUM cana-5883 141 48 4𝛽 4𝛽 NUM cana-5883 141 49 ) ) PUNCT cana-5883 141 50 2 2 NUM cana-5883 142 1 + + CCONJ cana-5883 142 2 ( ( PUNCT cana-5883 142 3 8Ο€ 8Ο€ X cana-5883 142 4 + + CCONJ cana-5883 142 5 2Ξ» 2Ξ» NUM cana-5883 142 6 ) ) PUNCT cana-5883 142 7 k2 k2 PROPN cana-5883 142 8 ( ( PUNCT cana-5883 142 9 2𝛽 2𝛽 NOUN cana-5883 142 10 βˆ’ βˆ’ PROPN cana-5883 143 1 [ [ X cana-5883 143 2 1 1 NUM cana-5883 143 3 Β± Β± NUM cana-5883 143 4 1 1 NUM cana-5883 143 5 + + CCONJ cana-5883 143 6 𝑍 𝑍 PROPN cana-5883 143 7 βˆšπ‘(𝑍 βˆšπ‘(𝑍 NOUN cana-5883 143 8 + + CCONJ cana-5883 143 9 2 2 NUM cana-5883 143 10 ) ) PUNCT cana-5883 143 11 + + CCONJ cana-5883 143 12 2 2 NUM cana-5883 143 13 ] ] PUNCT cana-5883 143 14 ) ) PUNCT cana-5883 144 1 3 3 NUM cana-5883 144 2 2𝛽2 2𝛽2 NUM cana-5883 144 3 Ξ» Ξ» NOUN cana-5883 144 4 [ [ PUNCT cana-5883 144 5 1 1 NUM cana-5883 144 6 Β± Β± NUM cana-5883 144 7 1 1 NUM cana-5883 144 8 + + CCONJ cana-5883 144 9 𝑧 𝑧 DET cana-5883 144 10 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 144 11 + + CCONJ cana-5883 144 12 2 2 X cana-5883 144 13 ) ) PUNCT cana-5883 144 14 + + CCONJ cana-5883 144 15 2 2 X cana-5883 144 16 ] ] SYM cana-5883 144 17 3 3 NUM cana-5883 144 18 4𝛽2 4𝛽2 NUM cana-5883 144 19 ( ( PUNCT cana-5883 144 20 4𝛽 4𝛽 NOUN cana-5883 144 21 βˆ’ βˆ’ PROPN cana-5883 145 1 [ [ X cana-5883 145 2 1 1 NUM cana-5883 145 3 Β± Β± NUM cana-5883 145 4 1 1 NUM cana-5883 145 5 + + CCONJ cana-5883 145 6 𝑧 𝑧 DET cana-5883 145 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 145 8 + + CCONJ cana-5883 145 9 2 2 X cana-5883 145 10 ) ) PUNCT cana-5883 145 11 + + CCONJ cana-5883 145 12 2 2 NUM cana-5883 145 13 ] ] PUNCT cana-5883 145 14 ) ) PUNCT cana-5883 145 15 3 3 NUM cana-5883 145 16 4𝛽2 4𝛽2 NUM cana-5883 146 1 βˆ’ βˆ’ NOUN cana-5883 146 2 8πλ 8πλ ADJ cana-5883 146 3 ( ( PUNCT cana-5883 146 4 2𝛽 2𝛽 NOUN cana-5883 146 5 βˆ’ βˆ’ PROPN cana-5883 147 1 [ [ X cana-5883 147 2 1 1 NUM cana-5883 147 3 Β± Β± NUM cana-5883 147 4 1 1 NUM cana-5883 147 5 + + CCONJ cana-5883 147 6 𝑧 𝑧 DET cana-5883 147 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 147 8 + + CCONJ cana-5883 147 9 2 2 X cana-5883 147 10 ) ) PUNCT cana-5883 147 11 + + CCONJ cana-5883 147 12 2 2 NUM cana-5883 147 13 ] ] PUNCT cana-5883 147 14 ) ) PUNCT cana-5883 147 15 1 1 NUM cana-5883 147 16 2𝛽2 2𝛽2 NUM cana-5883 147 17 [ [ X cana-5883 147 18 1 1 NUM cana-5883 147 19 Β± Β± NUM cana-5883 147 20 1 1 NUM cana-5883 147 21 + + CCONJ cana-5883 147 22 𝑧 𝑧 DET cana-5883 147 23 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 147 24 + + CCONJ cana-5883 147 25 2 2 X cana-5883 147 26 ) ) PUNCT cana-5883 147 27 + + CCONJ cana-5883 147 28 2 2 X cana-5883 147 29 ] ] SYM cana-5883 147 30 1 1 NUM cana-5883 147 31 4𝛽2 4𝛽2 NUM cana-5883 147 32 ( ( PUNCT cana-5883 147 33 4𝛽 4𝛽 NOUN cana-5883 147 34 βˆ’ βˆ’ PROPN cana-5883 148 1 [ [ X cana-5883 148 2 1 1 NUM cana-5883 148 3 Β± Β± NUM cana-5883 148 4 1 1 NUM cana-5883 148 5 + + CCONJ cana-5883 148 6 𝑧 𝑧 DET cana-5883 148 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 148 8 + + CCONJ cana-5883 148 9 2 2 X cana-5883 148 10 ) ) PUNCT cana-5883 148 11 + + CCONJ cana-5883 148 12 2 2 NUM cana-5883 148 13 ] ] PUNCT cana-5883 148 14 ) ) PUNCT cana-5883 148 15 1 1 NUM cana-5883 148 16 4𝛽2 4𝛽2 NOUN cana-5883 148 17 ] ] PUNCT cana-5883 148 18 [ [ PUNCT cana-5883 148 19 3πœ† 3πœ† NOUN cana-5883 148 20 [ [ X cana-5883 148 21 1 1 NUM cana-5883 148 22 Β± Β± NUM cana-5883 148 23 1 1 NUM cana-5883 148 24 + + CCONJ cana-5883 148 25 𝑧 𝑧 DET cana-5883 148 26 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 148 27 + + CCONJ cana-5883 148 28 2 2 X cana-5883 148 29 ) ) PUNCT cana-5883 148 30 + + CCONJ cana-5883 148 31 2 2 X cana-5883 148 32 ] ] SYM cana-5883 148 33 2 2 NUM cana-5883 148 34 βˆ’ βˆ’ NOUN cana-5883 148 35 12π›½πœ† 12π›½πœ† NOUN cana-5883 148 36 [ [ X cana-5883 148 37 1 1 NUM cana-5883 148 38 Β± Β± NUM cana-5883 148 39 1 1 NUM cana-5883 148 40 + + CCONJ cana-5883 148 41 𝑧 𝑧 DET cana-5883 148 42 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 148 43 + + CCONJ cana-5883 148 44 2 2 X cana-5883 148 45 ) ) PUNCT cana-5883 148 46 + + CCONJ cana-5883 148 47 2 2 NUM cana-5883 148 48 ] ] PUNCT cana-5883 148 49 + + CCONJ cana-5883 148 50 8 8 NUM cana-5883 148 51 πœ†π›½2 πœ†π›½2 NOUN cana-5883 148 52 βˆ’ βˆ’ PROPN cana-5883 148 53 ( ( PUNCT cana-5883 148 54 24Ο€ 24Ο€ NUM cana-5883 148 55 + + CCONJ cana-5883 148 56 3Ξ» 3Ξ» NUM cana-5883 148 57 ) ) PUNCT cana-5883 148 58 πœ† πœ† X cana-5883 149 1 [ [ X cana-5883 149 2 1 1 NUM cana-5883 149 3 Β± Β± NUM cana-5883 149 4 1 1 NUM cana-5883 149 5 + + CCONJ cana-5883 149 6 𝑧 𝑧 DET cana-5883 149 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 149 8 + + CCONJ cana-5883 149 9 2 2 X cana-5883 149 10 ) ) PUNCT cana-5883 149 11 + + CCONJ cana-5883 149 12 2 2 NUM cana-5883 149 13 ] ] SYM cana-5883 149 14 2 2 NUM cana-5883 149 15 ( ( PUNCT cana-5883 149 16 [ [ X cana-5883 149 17 1 1 NUM cana-5883 149 18 Β± Β± NUM cana-5883 149 19 1 1 NUM cana-5883 149 20 + + CCONJ cana-5883 149 21 𝑧 𝑧 DET cana-5883 149 22 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 149 23 + + CCONJ cana-5883 149 24 2 2 X cana-5883 149 25 ) ) PUNCT cana-5883 149 26 + + CCONJ cana-5883 149 27 2 2 X cana-5883 149 28 ] ] PUNCT cana-5883 149 29 βˆ’ βˆ’ NOUN cana-5883 149 30 2𝛽 2𝛽 NOUN cana-5883 149 31 ) ) PUNCT cana-5883 149 32 2 2 NUM cana-5883 149 33 ( ( PUNCT cana-5883 149 34 [ [ X cana-5883 149 35 1 1 NUM cana-5883 149 36 Β± Β± NUM cana-5883 149 37 1 1 NUM cana-5883 149 38 + + CCONJ cana-5883 149 39 𝑧 𝑧 DET cana-5883 149 40 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 149 41 + + CCONJ cana-5883 149 42 2 2 X cana-5883 149 43 ) ) PUNCT cana-5883 149 44 + + CCONJ cana-5883 149 45 2 2 X cana-5883 149 46 ] ] PUNCT cana-5883 149 47 βˆ’ βˆ’ NUM cana-5883 149 48 4𝛽 4𝛽 NUM cana-5883 149 49 ) ) PUNCT cana-5883 149 50 2 2 NUM cana-5883 149 51 + + CCONJ cana-5883 149 52 ( ( PUNCT cana-5883 149 53 8Ο€ 8Ο€ X cana-5883 149 54 + + CCONJ cana-5883 149 55 2Ξ» 2Ξ» NUM cana-5883 149 56 ) ) PUNCT cana-5883 149 57 k2 k2 PROPN cana-5883 149 58 ( ( PUNCT cana-5883 149 59 2𝛽 2𝛽 NOUN cana-5883 149 60 βˆ’ βˆ’ PROPN cana-5883 150 1 [ [ X cana-5883 150 2 1 1 NUM cana-5883 150 3 Β± Β± NUM cana-5883 150 4 1 1 NUM cana-5883 150 5 + + CCONJ cana-5883 150 6 𝑧 𝑧 DET cana-5883 150 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 150 8 + + CCONJ cana-5883 150 9 2 2 X cana-5883 150 10 ) ) PUNCT cana-5883 150 11 + + CCONJ cana-5883 150 12 2 2 NUM cana-5883 150 13 ] ] PUNCT cana-5883 150 14 ) ) PUNCT cana-5883 151 1 3 3 NUM cana-5883 151 2 2𝛽2 2𝛽2 NUM cana-5883 151 3 Ξ» Ξ» NOUN cana-5883 151 4 [ [ PUNCT cana-5883 151 5 1 1 NUM cana-5883 151 6 Β± Β± NUM cana-5883 151 7 1 1 NUM cana-5883 151 8 + + CCONJ cana-5883 151 9 𝑧 𝑧 DET cana-5883 151 10 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 151 11 + + CCONJ cana-5883 151 12 2 2 X cana-5883 151 13 ) ) PUNCT cana-5883 151 14 + + CCONJ cana-5883 151 15 2 2 X cana-5883 151 16 ] ] SYM cana-5883 151 17 3 3 NUM cana-5883 151 18 4𝛽2 4𝛽2 NUM cana-5883 151 19 ( ( PUNCT cana-5883 151 20 4𝛽 4𝛽 NOUN cana-5883 151 21 βˆ’ βˆ’ PROPN cana-5883 152 1 [ [ X cana-5883 152 2 1 1 NUM cana-5883 152 3 Β± Β± NUM cana-5883 152 4 1 1 NUM cana-5883 152 5 + + CCONJ cana-5883 152 6 𝑧 𝑧 DET cana-5883 152 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 152 8 + + CCONJ cana-5883 152 9 2 2 X cana-5883 152 10 ) ) PUNCT cana-5883 152 11 + + CCONJ cana-5883 152 12 2 2 NUM cana-5883 152 13 ] ] PUNCT cana-5883 152 14 ) ) PUNCT cana-5883 152 15 3 3 NUM cana-5883 152 16 4𝛽2 4𝛽2 NUM cana-5883 152 17 + + CCONJ cana-5883 152 18 ( ( PUNCT cana-5883 152 19 24Ο€ 24Ο€ NOUN cana-5883 152 20 + + CCONJ cana-5883 152 21 4Ξ» 4Ξ» PROPN cana-5883 152 22 ) ) PUNCT cana-5883 153 1 Ξ»(2𝛽 Ξ»(2𝛽 SYM cana-5883 153 2 βˆ’ βˆ’ PROPN cana-5883 154 1 [ [ X cana-5883 154 2 1 1 NUM cana-5883 154 3 Β± Β± NUM cana-5883 154 4 1 1 NUM cana-5883 154 5 + + CCONJ cana-5883 154 6 𝑧 𝑧 DET cana-5883 154 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 154 8 + + CCONJ cana-5883 154 9 2 2 X cana-5883 154 10 ) ) PUNCT cana-5883 154 11 + + CCONJ cana-5883 154 12 2 2 NUM cana-5883 154 13 ] ] PUNCT cana-5883 154 14 ) ) PUNCT cana-5883 154 15 1 1 NUM cana-5883 154 16 2𝛽2 2𝛽2 NUM cana-5883 154 17 [ [ X cana-5883 154 18 1 1 NUM cana-5883 154 19 Β± Β± NUM cana-5883 154 20 1 1 NUM cana-5883 154 21 + + CCONJ cana-5883 154 22 𝑧 𝑧 DET cana-5883 154 23 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 154 24 + + CCONJ cana-5883 154 25 2 2 X cana-5883 154 26 ) ) PUNCT cana-5883 154 27 + + CCONJ cana-5883 154 28 2 2 X cana-5883 154 29 ] ] SYM cana-5883 154 30 1 1 NUM cana-5883 154 31 4𝛽2 4𝛽2 NUM cana-5883 154 32 ( ( PUNCT cana-5883 154 33 4𝛽 4𝛽 NOUN cana-5883 154 34 βˆ’ βˆ’ PROPN cana-5883 155 1 [ [ X cana-5883 155 2 1 1 NUM cana-5883 155 3 Β± Β± NUM cana-5883 155 4 1 1 NUM cana-5883 155 5 + + CCONJ cana-5883 155 6 𝑧 𝑧 DET cana-5883 155 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 155 8 + + CCONJ cana-5883 155 9 2 2 X cana-5883 155 10 ) ) PUNCT cana-5883 155 11 + + CCONJ cana-5883 155 12 2 2 NUM cana-5883 155 13 ] ] PUNCT cana-5883 155 14 ) ) PUNCT cana-5883 155 15 1 1 NUM cana-5883 155 16 4𝛽2 4𝛽2 NOUN cana-5883 155 17 ] ] PUNCT cana-5883 155 18 ( ( PUNCT cana-5883 155 19 45 45 NUM cana-5883 155 20 ) ) PUNCT cana-5883 155 21 the the DET cana-5883 155 22 density density NOUN cana-5883 155 23 parameter parameter NOUN cana-5883 155 24 , , PUNCT cana-5883 155 25 Ο‰(t Ο‰(t NOUN cana-5883 155 26 ) ) PUNCT cana-5883 155 27 = = PUNCT cana-5883 155 28 𝜌 𝜌 X cana-5883 155 29 3𝐻2 3𝐻2 NUM cana-5883 155 30 Ο‰(t Ο‰(t NOUN cana-5883 155 31 ) ) PUNCT cana-5883 155 32 = = SYM cana-5883 156 1 2πœ†2𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 2πœ†2𝑑2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NUM cana-5883 156 2 3[(8Ο€+3Ξ»)2βˆ’Ξ»2 3[(8Ο€+3Ξ»)2βˆ’Ξ»2 NUM cana-5883 156 3 [ [ PUNCT cana-5883 156 4 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ 3πœ†π‘‘2βˆ’12π›½πœ†π‘‘ NUM cana-5883 156 5 + + SYM cana-5883 156 6 8 8 NUM cana-5883 156 7 πœ†π›½2βˆ’(24Ο€+3Ξ» πœ†π›½2βˆ’(24Ο€+3Ξ» NOUN cana-5883 156 8 ) ) PUNCT cana-5883 156 9 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 πœ†π‘‘2(2π›½βˆ’π‘‘)2(4π›½βˆ’π‘‘)2 NOUN cana-5883 157 1 + + CCONJ cana-5883 158 1 [ [ X cana-5883 158 2 ( ( PUNCT cana-5883 158 3 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 158 4 ) ) PUNCT cana-5883 158 5 ] ] PUNCT cana-5883 158 6 1 1 NUM cana-5883 158 7 2𝛽2 2𝛽2 NUM cana-5883 158 8 { { PUNCT cana-5883 158 9 ( ( PUNCT cana-5883 158 10 8Ο€+2Ξ» 8Ο€+2Ξ» NUM cana-5883 158 11 ) ) PUNCT cana-5883 158 12 k2 k2 PROPN cana-5883 158 13 [ [ X cana-5883 158 14 ( ( PUNCT cana-5883 158 15 2π›½βˆ’π‘‘ 2π›½βˆ’π‘‘ NUM cana-5883 158 16 ) ) PUNCT cana-5883 158 17 ] ] PUNCT cana-5883 158 18 1 1 NUM cana-5883 158 19 𝛽2 𝛽2 NOUN cana-5883 158 20 βˆ’(24Ο€+4Ξ» βˆ’(24Ο€+4Ξ» NUM cana-5883 158 21 ) ) PUNCT cana-5883 158 22 } } PUNCT cana-5883 158 23 λ𝑑 λ𝑑 VERB cana-5883 158 24 3 3 NUM cana-5883 158 25 4𝛽2(4π›½βˆ’π‘‘ 4𝛽2(4π›½βˆ’π‘‘ NOUN cana-5883 158 26 ) ) PUNCT cana-5883 158 27 ] ] PUNCT cana-5883 158 28 3 3 NUM cana-5883 158 29 4𝛽2 4𝛽2 NUM cana-5883 158 30 ] ] PUNCT cana-5883 158 31 ( ( PUNCT cana-5883 158 32 46 46 X cana-5883 158 33 ) ) PUNCT cana-5883 158 34 communications communication NOUN cana-5883 158 35 on on ADP cana-5883 158 36 applied apply VERB cana-5883 158 37 nonlinear nonlinear ADJ cana-5883 158 38 analysis analysis NOUN cana-5883 158 39 issn issn NOUN cana-5883 158 40 : : PUNCT cana-5883 158 41 1074 1074 NUM cana-5883 158 42 - - PUNCT cana-5883 158 43 133x 133x NUM cana-5883 158 44 vol vol NOUN cana-5883 158 45 32 32 NUM cana-5883 158 46 no no NOUN cana-5883 158 47 . . PUNCT cana-5883 159 1 2s 2s NUM cana-5883 159 2 ( ( PUNCT cana-5883 159 3 2025 2025 NUM cana-5883 159 4 ) ) PUNCT cana-5883 159 5 613 613 NUM cana-5883 159 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 159 7 density density NOUN cana-5883 159 8 parameter parameter NOUN cana-5883 159 9 in in ADP cana-5883 159 10 the the DET cana-5883 159 11 terms term NOUN cana-5883 159 12 of of ADP cana-5883 159 13 red red ADJ cana-5883 159 14 shift shift NOUN cana-5883 159 15 , , PUNCT cana-5883 159 16 Ο‰(z Ο‰(z PROPN cana-5883 159 17 ) ) PUNCT cana-5883 159 18 = = PUNCT cana-5883 160 1 2πœ†2 2πœ†2 NUM cana-5883 161 1 [ [ PUNCT cana-5883 161 2 1 1 NUM cana-5883 161 3 Β± Β± NUM cana-5883 161 4 1 1 NUM cana-5883 161 5 + + CCONJ cana-5883 161 6 𝑧 𝑧 DET cana-5883 161 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 161 8 + + CCONJ cana-5883 161 9 2 2 X cana-5883 161 10 ) ) PUNCT cana-5883 161 11 + + CCONJ cana-5883 161 12 2 2 NUM cana-5883 161 13 ] ] SYM cana-5883 161 14 2 2 NUM cana-5883 161 15 ( ( PUNCT cana-5883 161 16 [ [ X cana-5883 161 17 1 1 NUM cana-5883 161 18 Β± Β± NUM cana-5883 161 19 1 1 NUM cana-5883 161 20 + + CCONJ cana-5883 161 21 𝑧 𝑧 DET cana-5883 161 22 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 161 23 + + CCONJ cana-5883 161 24 2 2 X cana-5883 161 25 ) ) PUNCT cana-5883 161 26 + + CCONJ cana-5883 161 27 2 2 X cana-5883 161 28 ] ] PUNCT cana-5883 161 29 βˆ’ βˆ’ NOUN cana-5883 161 30 2𝛽 2𝛽 NOUN cana-5883 161 31 ) ) PUNCT cana-5883 161 32 2 2 NUM cana-5883 161 33 ( ( PUNCT cana-5883 161 34 [ [ X cana-5883 161 35 1 1 NUM cana-5883 161 36 Β± Β± NUM cana-5883 161 37 1 1 NUM cana-5883 161 38 + + CCONJ cana-5883 161 39 𝑧 𝑧 DET cana-5883 161 40 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 161 41 + + CCONJ cana-5883 161 42 2 2 X cana-5883 161 43 ) ) PUNCT cana-5883 161 44 + + CCONJ cana-5883 161 45 2 2 X cana-5883 161 46 ] ] PUNCT cana-5883 161 47 βˆ’ βˆ’ NUM cana-5883 161 48 4𝛽 4𝛽 NUM cana-5883 161 49 ) ) PUNCT cana-5883 161 50 2 2 NUM cana-5883 161 51 3[(8Ο€ 3[(8Ο€ NOUN cana-5883 161 52 + + NUM cana-5883 161 53 3Ξ»)2 3Ξ»)2 NUM cana-5883 161 54 βˆ’ βˆ’ NOUN cana-5883 161 55 Ξ»2 Ξ»2 NOUN cana-5883 161 56 [ [ PUNCT cana-5883 161 57 3πœ† 3πœ† NOUN cana-5883 161 58 [ [ X cana-5883 161 59 1 1 NUM cana-5883 161 60 Β± Β± NUM cana-5883 161 61 1 1 NUM cana-5883 161 62 + + CCONJ cana-5883 161 63 𝑧 𝑧 DET cana-5883 161 64 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 161 65 + + CCONJ cana-5883 161 66 2 2 X cana-5883 161 67 ) ) PUNCT cana-5883 161 68 + + CCONJ cana-5883 161 69 2 2 X cana-5883 161 70 ] ] SYM cana-5883 161 71 2 2 NUM cana-5883 161 72 βˆ’ βˆ’ NOUN cana-5883 161 73 12π›½πœ† 12π›½πœ† NOUN cana-5883 162 1 [ [ X cana-5883 162 2 1 1 NUM cana-5883 162 3 Β± Β± NUM cana-5883 162 4 1 1 NUM cana-5883 162 5 + + CCONJ cana-5883 162 6 𝑧 𝑧 DET cana-5883 162 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 162 8 + + CCONJ cana-5883 162 9 2 2 X cana-5883 162 10 ) ) PUNCT cana-5883 162 11 + + CCONJ cana-5883 162 12 2 2 NUM cana-5883 162 13 ] ] PUNCT cana-5883 162 14 + + CCONJ cana-5883 162 15 8 8 NUM cana-5883 162 16 πœ†π›½2 πœ†π›½2 NOUN cana-5883 162 17 βˆ’ βˆ’ PROPN cana-5883 162 18 ( ( PUNCT cana-5883 162 19 24Ο€ 24Ο€ NUM cana-5883 162 20 + + CCONJ cana-5883 162 21 3Ξ» 3Ξ» NUM cana-5883 162 22 ) ) PUNCT cana-5883 162 23 πœ† πœ† X cana-5883 163 1 [ [ X cana-5883 163 2 1 1 NUM cana-5883 163 3 Β± Β± NUM cana-5883 163 4 1 1 NUM cana-5883 163 5 + + CCONJ cana-5883 163 6 𝑧 𝑧 DET cana-5883 163 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 163 8 + + CCONJ cana-5883 163 9 2 2 X cana-5883 163 10 ) ) PUNCT cana-5883 163 11 + + CCONJ cana-5883 163 12 2 2 NUM cana-5883 163 13 ] ] SYM cana-5883 163 14 2 2 NUM cana-5883 163 15 ( ( PUNCT cana-5883 163 16 [ [ X cana-5883 163 17 1 1 NUM cana-5883 163 18 Β± Β± NUM cana-5883 163 19 1 1 NUM cana-5883 163 20 + + CCONJ cana-5883 163 21 𝑧 𝑧 DET cana-5883 163 22 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 163 23 + + CCONJ cana-5883 163 24 2 2 X cana-5883 163 25 ) ) PUNCT cana-5883 163 26 + + CCONJ cana-5883 163 27 2 2 X cana-5883 163 28 ] ] PUNCT cana-5883 163 29 βˆ’ βˆ’ NOUN cana-5883 163 30 2𝛽 2𝛽 NOUN cana-5883 163 31 ) ) PUNCT cana-5883 163 32 2 2 NUM cana-5883 163 33 ( ( PUNCT cana-5883 163 34 [ [ X cana-5883 163 35 1 1 NUM cana-5883 163 36 Β± Β± NUM cana-5883 163 37 1 1 NUM cana-5883 163 38 + + CCONJ cana-5883 163 39 𝑧 𝑧 DET cana-5883 163 40 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 163 41 + + CCONJ cana-5883 163 42 2 2 X cana-5883 163 43 ) ) PUNCT cana-5883 163 44 + + CCONJ cana-5883 163 45 2 2 X cana-5883 163 46 ] ] PUNCT cana-5883 163 47 βˆ’ βˆ’ NUM cana-5883 163 48 4𝛽 4𝛽 NUM cana-5883 163 49 ) ) PUNCT cana-5883 163 50 2 2 NUM cana-5883 163 51 + + CCONJ cana-5883 163 52 ( ( PUNCT cana-5883 163 53 2𝛽 2𝛽 NOUN cana-5883 163 54 βˆ’ βˆ’ PROPN cana-5883 164 1 [ [ X cana-5883 164 2 1 1 NUM cana-5883 164 3 Β± Β± NUM cana-5883 164 4 1 1 NUM cana-5883 164 5 + + CCONJ cana-5883 164 6 𝑧 𝑧 DET cana-5883 164 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 164 8 + + CCONJ cana-5883 164 9 2 2 X cana-5883 164 10 ) ) PUNCT cana-5883 164 11 + + CCONJ cana-5883 164 12 2 2 NUM cana-5883 164 13 ] ] PUNCT cana-5883 164 14 ) ) PUNCT cana-5883 164 15 1 1 NUM cana-5883 164 16 2𝛽2 2𝛽2 NUM cana-5883 164 17 { { PUNCT cana-5883 164 18 ( ( PUNCT cana-5883 164 19 8Ο€ 8Ο€ X cana-5883 164 20 + + CCONJ cana-5883 164 21 2Ξ» 2Ξ» NUM cana-5883 164 22 ) ) PUNCT cana-5883 164 23 k2 k2 PROPN cana-5883 164 24 [ [ X cana-5883 164 25 ( ( PUNCT cana-5883 164 26 2𝛽 2𝛽 NOUN cana-5883 164 27 βˆ’ βˆ’ PROPN cana-5883 165 1 [ [ X cana-5883 165 2 1 1 NUM cana-5883 165 3 Β± Β± NUM cana-5883 165 4 1 1 NUM cana-5883 165 5 + + CCONJ cana-5883 165 6 𝑧 𝑧 DET cana-5883 165 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 165 8 + + CCONJ cana-5883 165 9 2 2 X cana-5883 165 10 ) ) PUNCT cana-5883 165 11 + + CCONJ cana-5883 165 12 2 2 NUM cana-5883 165 13 ] ] PUNCT cana-5883 165 14 ) ) PUNCT cana-5883 165 15 ] ] PUNCT cana-5883 165 16 1 1 NUM cana-5883 165 17 𝛽2 𝛽2 PROPN cana-5883 165 18 βˆ’ βˆ’ PROPN cana-5883 165 19 ( ( PUNCT cana-5883 165 20 24Ο€ 24Ο€ NUM cana-5883 165 21 + + CCONJ cana-5883 165 22 4Ξ» 4Ξ» PROPN cana-5883 165 23 ) ) PUNCT cana-5883 166 1 Ξ» Ξ» X cana-5883 167 1 [ [ X cana-5883 167 2 1 1 NUM cana-5883 167 3 Β± Β± NUM cana-5883 167 4 1 1 NUM cana-5883 167 5 + + CCONJ cana-5883 167 6 𝑧 𝑧 DET cana-5883 167 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 167 8 + + CCONJ cana-5883 167 9 2 2 X cana-5883 167 10 ) ) PUNCT cana-5883 167 11 + + CCONJ cana-5883 167 12 2 2 X cana-5883 167 13 ] ] SYM cana-5883 167 14 3 3 NUM cana-5883 167 15 4𝛽2 4𝛽2 NUM cana-5883 167 16 ( ( PUNCT cana-5883 167 17 4𝛽 4𝛽 NOUN cana-5883 167 18 βˆ’ βˆ’ PROPN cana-5883 168 1 [ [ X cana-5883 168 2 1 1 NUM cana-5883 168 3 Β± Β± NUM cana-5883 168 4 1 1 NUM cana-5883 168 5 + + CCONJ cana-5883 168 6 𝑧 𝑧 DET cana-5883 168 7 βˆšπ‘§(𝑧 βˆšπ‘§(𝑧 NOUN cana-5883 168 8 + + CCONJ cana-5883 168 9 2 2 X cana-5883 168 10 ) ) PUNCT cana-5883 168 11 + + CCONJ cana-5883 168 12 2 2 NUM cana-5883 168 13 ] ] PUNCT cana-5883 168 14 ) ) PUNCT cana-5883 168 15 3 3 NUM cana-5883 168 16 4𝛽2 4𝛽2 NOUN cana-5883 168 17 ] ] PUNCT cana-5883 168 18 figure.1 figure.1 ADV cana-5883 168 19 average average ADJ cana-5883 168 20 scale scale NOUN cana-5883 168 21 factor factor NOUN cana-5883 168 22 ( ( PUNCT cana-5883 168 23 a a NOUN cana-5883 168 24 ) ) PUNCT cana-5883 168 25 against against ADP cana-5883 168 26 cosmic cosmic PROPN cana-5883 168 27 time(t time(t PROPN cana-5883 168 28 ) ) PUNCT cana-5883 168 29 communications communication NOUN cana-5883 168 30 on on ADP cana-5883 168 31 applied apply VERB cana-5883 168 32 nonlinear nonlinear ADJ cana-5883 168 33 analysis analysis NOUN cana-5883 168 34 issn issn NOUN cana-5883 168 35 : : PUNCT cana-5883 168 36 1074 1074 NUM cana-5883 168 37 - - PUNCT cana-5883 168 38 133x 133x NUM cana-5883 168 39 vol vol NOUN cana-5883 168 40 32 32 NUM cana-5883 168 41 no no NOUN cana-5883 168 42 . . PUNCT cana-5883 169 1 2s 2s NUM cana-5883 169 2 ( ( PUNCT cana-5883 169 3 2025 2025 NUM cana-5883 169 4 ) ) PUNCT cana-5883 169 5 614 614 NUM cana-5883 169 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 169 7 figure.2 figure.2 ADJ cana-5883 169 8 deceleration deceleration NOUN cana-5883 169 9 parameter parameter NOUN cana-5883 169 10 against against ADP cana-5883 169 11 cosmic cosmic PROPN cana-5883 169 12 time(t time(t PROPN cana-5883 169 13 ) ) PUNCT cana-5883 169 14 and and CCONJ cana-5883 169 15 redshift redshift NOUN cana-5883 169 16 ( ( PUNCT cana-5883 169 17 z z NOUN cana-5883 169 18 ) ) PUNCT cana-5883 169 19 figure figure NOUN cana-5883 169 20 3 3 NUM cana-5883 169 21 hubble hubble ADJ cana-5883 169 22 parameter parameter NOUN cana-5883 169 23 ( ( PUNCT cana-5883 169 24 h h NOUN cana-5883 169 25 ) ) PUNCT cana-5883 169 26 averse averse ADJ cana-5883 169 27 to to ADP cana-5883 169 28 cosmic cosmic PROPN cana-5883 169 29 time(t time(t PROPN cana-5883 169 30 ) ) PUNCT cana-5883 169 31 figure figure NOUN cana-5883 169 32 4 4 NUM cana-5883 169 33 . . PUNCT cana-5883 169 34 density density NOUN cana-5883 169 35 parameter parameter NOUN cana-5883 169 36 and and CCONJ cana-5883 169 37 pressure pressure NOUN cana-5883 169 38 against against ADP cana-5883 169 39 cosmic cosmic PROPN cana-5883 169 40 time(t time(t PROPN cana-5883 169 41 ) ) PUNCT cana-5883 169 42 communications communication NOUN cana-5883 169 43 on on ADP cana-5883 169 44 applied apply VERB cana-5883 169 45 nonlinear nonlinear ADJ cana-5883 169 46 analysis analysis NOUN cana-5883 169 47 issn issn NOUN cana-5883 169 48 : : PUNCT cana-5883 169 49 1074 1074 NUM cana-5883 169 50 - - PUNCT cana-5883 169 51 133x 133x NUM cana-5883 169 52 vol vol NOUN cana-5883 169 53 32 32 NUM cana-5883 169 54 no no NOUN cana-5883 169 55 . . PUNCT cana-5883 170 1 2s 2s NUM cana-5883 170 2 ( ( PUNCT cana-5883 170 3 2025 2025 NUM cana-5883 170 4 ) ) PUNCT cana-5883 170 5 615 615 NUM cana-5883 170 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 170 7 statefinder statefinder NOUN cana-5883 170 8 parameter parameter PROPN cana-5883 170 9 the the DET cana-5883 170 10 state state NOUN cana-5883 170 11 finder finder PROPN cana-5883 170 12 parameter parameter NOUN cana-5883 170 13 is be AUX cana-5883 170 14 decisive decisive ADJ cana-5883 170 15 in in ADP cana-5883 170 16 order order NOUN cana-5883 170 17 to to PART cana-5883 170 18 study study VERB cana-5883 170 19 the the DET cana-5883 170 20 cosmological cosmological ADJ cana-5883 170 21 models model NOUN cana-5883 170 22 . . PUNCT cana-5883 171 1 the the DET cana-5883 171 2 pair pair NOUN cana-5883 171 3 { { PUNCT cana-5883 171 4 r r NOUN cana-5883 171 5 , , PUNCT cana-5883 171 6 s s PART cana-5883 171 7 } } PUNCT cana-5883 171 8 is be AUX cana-5883 171 9 useful useful ADJ cana-5883 171 10 for for ADP cana-5883 171 11 distinguishing distinguish VERB cana-5883 171 12 the the DET cana-5883 171 13 properties property NOUN cana-5883 171 14 of of ADP cana-5883 171 15 dark dark ADJ cana-5883 171 16 energy energy NOUN cana-5883 171 17 . . PUNCT cana-5883 172 1 the the DET cana-5883 172 2 r r NOUN cana-5883 172 3 βˆ’ βˆ’ PROPN cana-5883 172 4 s s PART cana-5883 172 5 plane plane NOUN cana-5883 172 6 advisable advisable ADJ cana-5883 172 7 the the DET cana-5883 172 8 different different ADJ cana-5883 172 9 qualitative qualitative ADJ cana-5883 172 10 behaviour behaviour NOUN cana-5883 172 11 for for ADP cana-5883 172 12 different different ADJ cana-5883 172 13 cosmological cosmological ADJ cana-5883 172 14 models model NOUN cana-5883 172 15 . . PUNCT cana-5883 173 1 the the DET cana-5883 173 2 state state NOUN cana-5883 173 3 appropriator appropriator NOUN cana-5883 173 4 diagnostic diagnostic ADJ cana-5883 173 5 along along ADP cana-5883 173 6 with with ADP cana-5883 173 7 snap snap NOUN cana-5883 173 8 ( ( PUNCT cana-5883 173 9 super super X cana-5883 173 10 novae novae ADJ cana-5883 173 11 acceleration acceleration NOUN cana-5883 173 12 probe probe NOUN cana-5883 173 13 ) ) PUNCT cana-5883 173 14 inspection inspection NOUN cana-5883 173 15 may may AUX cana-5883 173 16 distinguish distinguish VERB cana-5883 173 17 different different ADJ cana-5883 173 18 dark dark ADJ cana-5883 173 19 energy energy NOUN cana-5883 173 20 models model NOUN cana-5883 173 21 . . PUNCT cana-5883 174 1 the the DET cana-5883 174 2 state state NOUN cana-5883 174 3 finder finder NOUN cana-5883 174 4 pair pair NOUN cana-5883 174 5 { { PUNCT cana-5883 174 6 r r NOUN cana-5883 174 7 , , PUNCT cana-5883 174 8 s s AUX cana-5883 174 9 } } PUNCT cana-5883 174 10 is be AUX cana-5883 174 11 defined define VERB cana-5883 174 12 as as ADP cana-5883 174 13 , , PUNCT cana-5883 174 14 r r NOUN cana-5883 174 15 = = SYM cana-5883 174 16 π‘Ž π‘Ž X cana-5883 174 17 π‘Žπ»3 π‘Žπ»3 PROPN cana-5883 174 18 together together ADV cana-5883 174 19 with with ADP cana-5883 174 20 s s PROPN cana-5883 174 21 = = PUNCT cana-5883 174 22 π‘Ÿβˆ’1 π‘Ÿβˆ’1 PROPN cana-5883 174 23 3(π‘žβˆ’0.5 3(π‘žβˆ’0.5 NUM cana-5883 174 24 ) ) PUNCT cana-5883 174 25 here here ADV cana-5883 174 26 , , PUNCT cana-5883 174 27 the the DET cana-5883 174 28 associated associate VERB cana-5883 174 29 with with ADP cana-5883 174 30 parameters parameter NOUN cana-5883 174 31 have have VERB cana-5883 174 32 the the DET cana-5883 174 33 accustomed accustomed ADJ cana-5883 174 34 denotation denotation NOUN cana-5883 174 35 talk talk NOUN cana-5883 174 36 throughout throughout ADP cana-5883 174 37 the the DET cana-5883 174 38 paper paper NOUN cana-5883 174 39 . . PUNCT cana-5883 175 1 the the DET cana-5883 175 2 state state NOUN cana-5883 175 3 finder finder NOUN cana-5883 175 4 parameters parameter NOUN cana-5883 175 5 for for ADP cana-5883 175 6 the the DET cana-5883 175 7 discussed discuss VERB cana-5883 175 8 model model NOUN cana-5883 175 9 are be AUX cana-5883 175 10 obtained obtain VERB cana-5883 175 11 as as ADP cana-5883 175 12 , , PUNCT cana-5883 175 13 r r NOUN cana-5883 175 14 = = SYM cana-5883 176 1 π‘Ž π‘Ž PRON cana-5883 176 2 π‘Žπ»3 π‘Žπ»3 PROPN cana-5883 176 3 = = SYM cana-5883 176 4 𝑧2 𝑧2 PROPN cana-5883 176 5 + + PROPN cana-5883 176 6 2π‘§βˆ’1 2π‘§βˆ’1 NUM cana-5883 176 7 𝑧2 𝑧2 NOUN cana-5883 176 8 + + NOUN cana-5883 176 9 2𝑧+2 2𝑧+2 PROPN cana-5883 176 10 [ [ X cana-5883 176 11 2 2 NUM cana-5883 176 12 ( ( PUNCT cana-5883 176 13 𝑧2 𝑧2 NOUN cana-5883 176 14 + + PROPN cana-5883 176 15 2π‘§βˆ’1 2π‘§βˆ’1 NUM cana-5883 176 16 𝑧2 𝑧2 NOUN cana-5883 176 17 + + NOUN cana-5883 176 18 2𝑧+2 2𝑧+2 NUM cana-5883 176 19 ) ) PUNCT cana-5883 177 1 + + CCONJ cana-5883 178 1 1 1 X cana-5883 178 2 ] ] X cana-5883 178 3 + + CCONJ cana-5883 178 4 6(1+z)2 6(1+z)2 NUM cana-5883 178 5 ( ( PUNCT cana-5883 178 6 𝑧2 𝑧2 NOUN cana-5883 178 7 + + NOUN cana-5883 178 8 2𝑧+2)2 2𝑧+2)2 NUM cana-5883 178 9 s s PART cana-5883 178 10 = = SYM cana-5883 178 11 βˆ’18 βˆ’18 PROPN cana-5883 178 12 ( ( PUNCT cana-5883 178 13 1+z)2 1+z)2 NOUN cana-5883 178 14 ( ( PUNCT cana-5883 178 15 2𝑧2 2𝑧2 NUM cana-5883 178 16 + + NOUN cana-5883 178 17 4𝑧+1 4𝑧+1 NOUN cana-5883 178 18 ) ) PUNCT cana-5883 178 19 ( ( PUNCT cana-5883 178 20 𝑧2 𝑧2 NOUN cana-5883 178 21 + + NOUN cana-5883 178 22 2𝑧+2)2 2𝑧+2)2 NUM cana-5883 178 23 + + CCONJ cana-5883 178 24 3𝑧 3𝑧 NOUN cana-5883 178 25 ( ( PUNCT cana-5883 178 26 𝑧2 𝑧2 NOUN cana-5883 178 27 + + NOUN cana-5883 178 28 2π‘§βˆ’1 2π‘§βˆ’1 NUM cana-5883 178 29 ) ) PUNCT cana-5883 178 30 ( ( PUNCT cana-5883 178 31 𝑧+2 𝑧+2 NUM cana-5883 178 32 ) ) PUNCT cana-5883 178 33 ( ( PUNCT cana-5883 178 34 5𝑧2 5𝑧2 NUM cana-5883 178 35 + + NOUN cana-5883 178 36 10𝑧+1 10𝑧+1 NUM cana-5883 178 37 ) ) PUNCT cana-5883 178 38 ( ( PUNCT cana-5883 178 39 𝑧2 𝑧2 NOUN cana-5883 178 40 + + PROPN cana-5883 178 41 2𝑧+2)3 2𝑧+2)3 NUM cana-5883 178 42 iv iv NOUN cana-5883 178 43 . . PUNCT cana-5883 178 44 result result NOUN cana-5883 178 45 and and CCONJ cana-5883 178 46 discussion discussion NOUN cana-5883 178 47 in in ADP cana-5883 178 48 the the DET cana-5883 178 49 figure1 figure1 PROPN cana-5883 178 50 , , PUNCT cana-5883 178 51 opposed oppose VERB cana-5883 178 52 to to ADP cana-5883 178 53 time time NOUN cana-5883 178 54 we we PRON cana-5883 178 55 have have AUX cana-5883 178 56 taken take VERB cana-5883 178 57 the the DET cana-5883 178 58 interval interval NOUN cana-5883 178 59 [ [ X cana-5883 178 60 0 0 NUM cana-5883 178 61 , , PUNCT cana-5883 178 62 2 2 NUM cana-5883 178 63 ] ] PUNCT cana-5883 178 64 for for ADP cana-5883 178 65 cosmic cosmic ADJ cana-5883 178 66 time time NOUN cana-5883 178 67 , , PUNCT cana-5883 178 68 while while SCONJ cana-5883 178 69 the the DET cana-5883 178 70 roughly roughly ADV cana-5883 178 71 is be AUX cana-5883 178 72 notable notable ADJ cana-5883 178 73 in in ADP cana-5883 178 74 interval interval NOUN cana-5883 178 75 [ [ X cana-5883 178 76 0,1 0,1 NUM cana-5883 178 77 ] ] PUNCT cana-5883 178 78 only only ADV cana-5883 178 79 . . PUNCT cana-5883 179 1 noteworthy noteworthy ADJ cana-5883 179 2 this this PRON cana-5883 179 3 , , PUNCT cana-5883 179 4 the the DET cana-5883 179 5 creativity creativity NOUN cana-5883 179 6 from from ADP cana-5883 179 7 the the DET cana-5883 179 8 value value NOUN cana-5883 179 9 of of ADP cana-5883 179 10 scale scale NOUN cana-5883 179 11 factor factor NOUN cana-5883 179 12 i.e. i.e. X cana-5883 179 13 , , PUNCT cana-5883 179 14 scale scale NOUN cana-5883 179 15 factor factor NOUN cana-5883 179 16 is be AUX cana-5883 179 17 negative negative ADJ cana-5883 179 18 in in ADP cana-5883 179 19 the the DET cana-5883 179 20 domain domain NOUN cana-5883 179 21 [ [ X cana-5883 179 22 1,2 1,2 NUM cana-5883 179 23 ] ] PUNCT cana-5883 179 24 . . PUNCT cana-5883 180 1 so so ADV cana-5883 180 2 that that SCONJ cana-5883 180 3 this this DET cana-5883 180 4 region region NOUN cana-5883 180 5 is be AUX cana-5883 180 6 insignificant insignificant ADJ cana-5883 180 7 from from ADP cana-5883 180 8 the the DET cana-5883 180 9 observed observed ADJ cana-5883 180 10 value value NOUN cana-5883 180 11 . . PUNCT cana-5883 181 1 figure figure NOUN cana-5883 181 2 2 2 NUM cana-5883 181 3 , , PUNCT cana-5883 181 4 represents represent VERB cana-5883 181 5 behaviour behaviour NOUN cana-5883 181 6 of of ADP cana-5883 181 7 the the DET cana-5883 181 8 deceleration deceleration NOUN cana-5883 181 9 parameter parameter NOUN cana-5883 181 10 hostile hostile NOUN cana-5883 181 11 to to ADP cana-5883 181 12 cosmic cosmic ADJ cana-5883 181 13 time time NOUN cana-5883 181 14 and and CCONJ cana-5883 181 15 red red ADJ cana-5883 181 16 shift shift NOUN cana-5883 181 17 separately separately ADV cana-5883 181 18 from from ADP cana-5883 181 19 the the DET cana-5883 181 20 figures figure NOUN cana-5883 181 21 for for ADP cana-5883 181 22 equation equation NOUN cana-5883 181 23 ( ( PUNCT cana-5883 181 24 29 29 NUM cana-5883 181 25 ) ) PUNCT cana-5883 181 26 , , PUNCT cana-5883 181 27 it it PRON cana-5883 181 28 can can AUX cana-5883 181 29 be be AUX cana-5883 181 30 observed observe VERB cana-5883 181 31 that that SCONJ cana-5883 181 32 at at ADP cana-5883 181 33 𝛽 𝛽 NOUN cana-5883 181 34 = = SYM cana-5883 181 35 1/2 1/2 NUM cana-5883 181 36 , , PUNCT cana-5883 181 37 the the DET cana-5883 181 38 deceleration deceleration NOUN cana-5883 181 39 parameter parameter NOUN cana-5883 181 40 starts start VERB cana-5883 181 41 at at ADP cana-5883 181 42 q q NOUN cana-5883 181 43 = = SYM cana-5883 181 44 1 1 NUM cana-5883 181 45 at at ADP cana-5883 181 46 initial initial ADJ cana-5883 181 47 time time NOUN cana-5883 181 48 t t PROPN cana-5883 181 49 = = SYM cana-5883 181 50 0 0 PUNCT cana-5883 181 51 and and CCONJ cana-5883 181 52 ends end VERB cana-5883 181 53 at at ADP cana-5883 181 54 q= q= ADV cana-5883 181 55 -2 -2 INTJ cana-5883 181 56 at at ADP cana-5883 181 57 t t NOUN cana-5883 181 58 = = PROPN cana-5883 181 59 1 1 NUM cana-5883 181 60 . . PUNCT cana-5883 182 1 so so ADV cana-5883 182 2 , , PUNCT cana-5883 182 3 observations observation NOUN cana-5883 182 4 show show VERB cana-5883 182 5 that that SCONJ cana-5883 182 6 deceleration deceleration NOUN cana-5883 182 7 parameter parameter NOUN cana-5883 182 8 be be AUX cana-5883 182 9 sited site VERB cana-5883 182 10 in in ADP cana-5883 182 11 the the DET cana-5883 182 12 interval interval NOUN cana-5883 183 1 [ [ X cana-5883 183 2 -2,1 -2,1 X cana-5883 183 3 ] ] X cana-5883 183 4 for for ADP cana-5883 183 5 the the DET cana-5883 183 6 time time NOUN cana-5883 183 7 interval interval NOUN cana-5883 183 8 [ [ X cana-5883 183 9 0,1 0,1 NOUN cana-5883 183 10 ] ] PUNCT cana-5883 183 11 . . PUNCT cana-5883 184 1 in in ADP cana-5883 184 2 the the DET cana-5883 184 3 course course NOUN cana-5883 184 4 of of ADP cana-5883 184 5 the the DET cana-5883 184 6 time time NOUN cana-5883 184 7 interval interval NOUN cana-5883 184 8 of of ADP cana-5883 184 9 t t PROPN cana-5883 184 10 ∈ ∈ PROPN cana-5883 184 11 [ [ X cana-5883 184 12 0,0.18 0,0.18 X cana-5883 184 13 ] ] X cana-5883 184 14 , , PUNCT cana-5883 184 15 q q X cana-5883 184 16 is be AUX cana-5883 184 17 positive positive ADJ cana-5883 184 18 . . PUNCT cana-5883 184 19 , , PUNCT cana-5883 184 20 q q PROPN cana-5883 184 21 lies lie VERB cana-5883 184 22 between between ADP cana-5883 184 23 [ [ X cana-5883 184 24 1 1 NUM cana-5883 184 25 , , PUNCT cana-5883 184 26 0.0172 0.0172 NUM cana-5883 184 27 ] ] PUNCT cana-5883 184 28 which which PRON cana-5883 184 29 advisable advisable VERB cana-5883 184 30 the the DET cana-5883 184 31 decelerating decelerate VERB cana-5883 184 32 phase phase NOUN cana-5883 184 33 . . PUNCT cana-5883 185 1 i.e. i.e. X cana-5883 185 2 ( ( PUNCT cana-5883 185 3 q q NOUN cana-5883 185 4 > > X cana-5883 185 5 0 0 NUM cana-5883 185 6 ) ) PUNCT cana-5883 185 7 . . PUNCT cana-5883 186 1 at at ADP cana-5883 186 2 t t PROPN cana-5883 186 3 = = SYM cana-5883 186 4 0.19 0.19 NUM cana-5883 186 5 , , PUNCT cana-5883 186 6 q q PROPN cana-5883 186 7 is be AUX cana-5883 186 8 negative negative ADJ cana-5883 186 9 , , PUNCT cana-5883 186 10 which which PRON cana-5883 186 11 indicates indicate VERB cana-5883 186 12 the the DET cana-5883 186 13 accelerating accelerate VERB cana-5883 186 14 phase phase NOUN cana-5883 186 15 . . PUNCT cana-5883 187 1 i.e. i.e. X cana-5883 187 2 ( ( PUNCT cana-5883 187 3 q q X cana-5883 187 4 < < X cana-5883 187 5 0 0 NUM cana-5883 187 6 ) ) PUNCT cana-5883 187 7 . . PUNCT cana-5883 188 1 in in ADP cana-5883 188 2 the the DET cana-5883 188 3 interval interval NOUN cana-5883 188 4 t t PROPN cana-5883 188 5 ∈ ∈ PROPN cana-5883 189 1 [ [ X cana-5883 189 2 1 1 NUM cana-5883 189 3 , , PUNCT cana-5883 189 4 1.57 1.57 NUM cana-5883 189 5 ] ] PUNCT cana-5883 189 6 present present ADJ cana-5883 189 7 model model NOUN cana-5883 189 8 forecasting forecast VERB cana-5883 189 9 the the DET cana-5883 189 10 super super ADJ cana-5883 189 11 exponential exponential ADJ cana-5883 189 12 phase phase NOUN cana-5883 189 13 i.e. i.e. X cana-5883 189 14 , , PUNCT cana-5883 189 15 ( ( PUNCT cana-5883 189 16 q q X cana-5883 189 17 < < X cana-5883 189 18 -1 -1 NOUN cana-5883 189 19 ) ) PUNCT cana-5883 189 20 . . PUNCT cana-5883 190 1 the the DET cana-5883 190 2 qualitative qualitative ADJ cana-5883 190 3 behaviour behaviour NOUN cana-5883 190 4 of of ADP cana-5883 190 5 q(z q(z PROPN cana-5883 190 6 ) ) PUNCT cana-5883 190 7 is be AUX cana-5883 190 8 consistent consistent ADJ cana-5883 190 9 with with ADP cana-5883 190 10 deceleration deceleration NOUN cana-5883 190 11 parameter parameter NOUN cana-5883 190 12 discussed discuss VERB cana-5883 190 13 by by ADP cana-5883 190 14 farook farook NOUN cana-5883 190 15 [ [ X cana-5883 190 16 43 43 NUM cana-5883 190 17 ] ] PUNCT cana-5883 190 18 . . PUNCT cana-5883 191 1 figure figure NOUN cana-5883 191 2 3 3 NUM cana-5883 191 3 represents represent VERB cana-5883 191 4 the the DET cana-5883 191 5 hubble hubble ADJ cana-5883 191 6 parameter parameter NOUN cana-5883 191 7 against against ADP cana-5883 191 8 cosmic cosmic ADJ cana-5883 191 9 time time NOUN cana-5883 191 10 which which PRON cana-5883 191 11 shows show VERB cana-5883 191 12 that that SCONJ cana-5883 191 13 , , PUNCT cana-5883 191 14 h h NOUN cana-5883 191 15 diverges diverge VERB cana-5883 191 16 at at ADP cana-5883 191 17 t t NOUN cana-5883 191 18 = = SYM cana-5883 191 19 0 0 PROPN cana-5883 191 20 and and CCONJ cana-5883 191 21 t t X cana-5883 191 22 = = SYM cana-5883 191 23 2 2 NUM cana-5883 191 24 𝛽 𝛽 NOUN cana-5883 191 25 , , PUNCT cana-5883 191 26 i.e. i.e. X cana-5883 191 27 , , PUNCT cana-5883 191 28 t t NOUN cana-5883 191 29 = = SYM cana-5883 191 30 1 1 X cana-5883 191 31 . . PUNCT cana-5883 191 32 further far ADV cana-5883 191 33 , , PUNCT cana-5883 191 34 one one PRON cana-5883 191 35 can can AUX cana-5883 191 36 say say VERB cana-5883 191 37 that that SCONJ cana-5883 191 38 the the DET cana-5883 191 39 big big ADJ cana-5883 191 40 rip rip NOUN cana-5883 191 41 moment moment NOUN cana-5883 191 42 occurs occur VERB cana-5883 191 43 at at ADP cana-5883 191 44 t t PROPN cana-5883 191 45 = = SYM cana-5883 191 46 1 1 X cana-5883 191 47 . . X cana-5883 191 48 figure figure NOUN cana-5883 191 49 4 4 NUM cana-5883 191 50 , , PUNCT cana-5883 191 51 characterized characterize VERB cana-5883 191 52 the the DET cana-5883 191 53 variation variation NOUN cana-5883 191 54 of of ADP cana-5883 191 55 the the DET cana-5883 191 56 energy energy NOUN cana-5883 191 57 density density NOUN cana-5883 191 58 and and CCONJ cana-5883 191 59 pressure pressure NOUN cana-5883 191 60 of of ADP cana-5883 191 61 model model NOUN cana-5883 191 62 for for ADP cana-5883 191 63 the the DET cana-5883 191 64 flat flat ADJ cana-5883 191 65 , , PUNCT cana-5883 191 66 open open ADJ cana-5883 191 67 and and CCONJ cana-5883 191 68 closed closed ADJ cana-5883 191 69 universe universe NOUN cana-5883 191 70 [ [ X cana-5883 191 71 44 44 NUM cana-5883 191 72 ] ] PUNCT cana-5883 191 73 . . PUNCT cana-5883 192 1 it it PRON cana-5883 192 2 is be AUX cana-5883 192 3 strong strong ADJ cana-5883 192 4 matches match NOUN cana-5883 192 5 out out ADP cana-5883 192 6 that that SCONJ cana-5883 192 7 in in ADP cana-5883 192 8 both both CCONJ cana-5883 192 9 the the DET cana-5883 192 10 models model NOUN cana-5883 192 11 , , PUNCT cana-5883 192 12 for for ADP cana-5883 192 13 flat flat ADJ cana-5883 192 14 , , PUNCT cana-5883 192 15 open open ADJ cana-5883 192 16 and and CCONJ cana-5883 192 17 closed closed ADJ cana-5883 192 18 universes universe NOUN cana-5883 192 19 , , PUNCT cana-5883 192 20 the the DET cana-5883 192 21 energy energy NOUN cana-5883 192 22 density density NOUN cana-5883 192 23 has have VERB cana-5883 192 24 singularities singularity NOUN cana-5883 192 25 at at ADP cana-5883 192 26 t t NOUN cana-5883 192 27 = = SYM cana-5883 192 28 0 0 PROPN cana-5883 192 29 and and CCONJ cana-5883 192 30 t t X cana-5883 192 31 = = SYM cana-5883 192 32 1 1 NUM cana-5883 192 33 , , PUNCT cana-5883 192 34 is be AUX cana-5883 192 35 non non ADJ cana-5883 192 36 - - ADJ cana-5883 192 37 negative negative ADJ cana-5883 192 38 ( ( PUNCT cana-5883 192 39 𝜌 𝜌 X cana-5883 192 40 β‰₯ β‰₯ NOUN cana-5883 192 41 0 0 NUM cana-5883 192 42 ) ) PUNCT cana-5883 192 43 . . PUNCT cana-5883 193 1 the the DET cana-5883 193 2 energy energy NOUN cana-5883 193 3 density density NOUN cana-5883 193 4 in in ADP cana-5883 193 5 all all PRON cana-5883 193 6 flat flat ADJ cana-5883 193 7 , , PUNCT cana-5883 193 8 open open ADJ cana-5883 193 9 and and CCONJ cana-5883 193 10 closed closed ADJ cana-5883 193 11 universes universe NOUN cana-5883 193 12 has have VERB cana-5883 193 13 a a DET cana-5883 193 14 big big ADJ cana-5883 193 15 rip rip ADJ cana-5883 193 16 moment moment NOUN cana-5883 193 17 at at ADP cana-5883 193 18 t t NOUN cana-5883 193 19 = = SYM cana-5883 193 20 1 1 NUM cana-5883 193 21 due due ADP cana-5883 193 22 to to ADP cana-5883 193 23 the the DET cana-5883 193 24 divergent divergent ADJ cana-5883 193 25 essence essence NOUN cana-5883 193 26 of of ADP cana-5883 193 27 the the DET cana-5883 193 28 scale scale NOUN cana-5883 193 29 factor factor NOUN cana-5883 193 30 and and CCONJ cana-5883 193 31 energy energy NOUN cana-5883 193 32 density density NOUN cana-5883 193 33 of of ADP cana-5883 193 34 the the DET cana-5883 193 35 fluid fluid NOUN cana-5883 193 36 at at ADP cana-5883 193 37 that that DET cana-5883 193 38 time time NOUN cana-5883 193 39 . . PUNCT cana-5883 194 1 at at ADP cana-5883 194 2 the the DET cana-5883 194 3 initial initial ADJ cana-5883 194 4 point point NOUN cana-5883 194 5 t t PROPN cana-5883 194 6 = = SYM cana-5883 194 7 0 0 PROPN cana-5883 194 8 , , PUNCT cana-5883 194 9 the the DET cana-5883 194 10 pressure pressure NOUN cana-5883 194 11 has have VERB cana-5883 194 12 the the DET cana-5883 194 13 maximum maximum ADJ cana-5883 194 14 value value NOUN cana-5883 194 15 . . PUNCT cana-5883 195 1 the the DET cana-5883 195 2 pressure pressure NOUN cana-5883 195 3 is be AUX cana-5883 195 4 positive positive ADJ cana-5883 195 5 valued value VERB cana-5883 195 6 in in ADP cana-5883 195 7 the the DET cana-5883 195 8 interval interval NOUN cana-5883 195 9 [ [ X cana-5883 195 10 0 0 NUM cana-5883 195 11 , , PUNCT cana-5883 195 12 0.08 0.08 NUM cana-5883 195 13 ] ] PUNCT cana-5883 195 14 and and CCONJ cana-5883 195 15 negative negative ADJ cana-5883 195 16 valued value VERB cana-5883 195 17 in in ADP cana-5883 195 18 the the DET cana-5883 195 19 interval interval NOUN cana-5883 195 20 [ [ X cana-5883 195 21 0.09 0.09 NUM cana-5883 195 22 , , PUNCT cana-5883 195 23 1 1 NUM cana-5883 195 24 ] ] PUNCT cana-5883 195 25 . . PUNCT cana-5883 196 1 for for ADP cana-5883 196 2 the the DET cana-5883 196 3 closed closed ADJ cana-5883 196 4 universe universe NOUN cana-5883 196 5 of of ADP cana-5883 196 6 the the DET cana-5883 196 7 model model NOUN cana-5883 196 8 . . PUNCT cana-5883 197 1 communications communication NOUN cana-5883 197 2 on on ADP cana-5883 197 3 applied apply VERB cana-5883 197 4 nonlinear nonlinear ADJ cana-5883 197 5 analysis analysis NOUN cana-5883 197 6 issn issn NOUN cana-5883 197 7 : : PUNCT cana-5883 197 8 1074 1074 NUM cana-5883 197 9 - - PUNCT cana-5883 197 10 133x 133x NUM cana-5883 197 11 vol vol NOUN cana-5883 197 12 32 32 NUM cana-5883 197 13 no no NOUN cana-5883 197 14 . . PUNCT cana-5883 198 1 2s 2s NUM cana-5883 198 2 ( ( PUNCT cana-5883 198 3 2025 2025 NUM cana-5883 198 4 ) ) PUNCT cana-5883 198 5 616 616 NUM cana-5883 198 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 198 7 v. v. ADP cana-5883 198 8 references reference NOUN cana-5883 198 9 : : PUNCT cana-5883 198 10 1 1 X cana-5883 198 11 . . X cana-5883 198 12 riess riess PROPN cana-5883 198 13 a.g a.g PROPN cana-5883 198 14 . . PROPN cana-5883 198 15 et et PROPN cana-5883 198 16 . . PUNCT cana-5883 199 1 al al PROPN cana-5883 199 2 . . PROPN cana-5883 199 3 , , PUNCT cana-5883 199 4 1998 1998 NUM cana-5883 199 5 . . PUNCT cana-5883 200 1 observational observational ADJ cana-5883 200 2 evidence evidence NOUN cana-5883 200 3 from from ADP cana-5883 200 4 supernovae supernovae NOUN cana-5883 200 5 for for ADP cana-5883 200 6 an an DET cana-5883 200 7 acceleratinguniverse acceleratinguniverse NOUN cana-5883 200 8 and and CCONJ cana-5883 200 9 a a DET cana-5883 200 10 cosmological cosmological ADJ cana-5883 200 11 constant.astronomical constant.astronomical ADJ cana-5883 200 12 journal journal NOUN cana-5883 200 13 . . PUNCT cana-5883 201 1 1161009 1161009 NUM cana-5883 201 2 . . PUNCT cana-5883 202 1 https://doi.org/10.1086/300499 https://doi.org/10.1086/300499 NOUN cana-5883 202 2 2.perlmutter 2.perlmutter NUM cana-5883 202 3 , , PUNCT cana-5883 202 4 s. s. PROPN cana-5883 202 5 , , PUNCT cana-5883 202 6 et et PROPN cana-5883 202 7 al al PROPN cana-5883 202 8 . . PROPN cana-5883 202 9 , , PUNCT cana-5883 202 10 1999 1999 NUM cana-5883 202 11 . . PUNCT cana-5883 203 1 measurements measurement NOUN cana-5883 203 2 of of ADP cana-5883 203 3 Ο‰ Ο‰ NUM cana-5883 203 4 and and CCONJ cana-5883 203 5 Ξ» Ξ» PROPN cana-5883 203 6 from from ADP cana-5883 203 7 42 42 NUM cana-5883 203 8 high high ADJ cana-5883 203 9 - - PUNCT cana-5883 203 10 redshift redshift NOUN cana-5883 203 11 supernovae.astrophys supernovae.astrophy NOUN cana-5883 203 12 . . PUNCT cana-5883 204 1 j. j. PROPN cana-5883 204 2 517 517 PROPN cana-5883 204 3 , , PUNCT cana-5883 204 4 565.https://doi.org/10.1086/307221 565.https://doi.org/10.1086/307221 PROPN cana-5883 204 5 3.percival 3.percival NUM cana-5883 204 6 , , PUNCT cana-5883 204 7 w. w. PROPN cana-5883 204 8 j. j. PROPN cana-5883 204 9 ,2001.the ,2001.the PROPN cana-5883 204 10 2df 2df PROPN cana-5883 204 11 galaxy galaxy PROPN cana-5883 204 12 redshift redshift NOUN cana-5883 204 13 survey survey NOUN cana-5883 204 14 : : PUNCT cana-5883 204 15 the the DET cana-5883 204 16 power power NOUN cana-5883 204 17 spectrum spectrum NOUN cana-5883 204 18 and and CCONJ cana-5883 204 19 the the DET cana-5883 204 20 matter matter NOUN cana-5883 204 21 content content NOUN cana-5883 204 22 of of ADP cana-5883 204 23 the the DET cana-5883 204 24 universe.royal universe.royal PROPN cana-5883 204 25 astronomical astronomical ADJ cana-5883 204 26 society society NOUN cana-5883 204 27 , , PUNCT cana-5883 204 28 327 327 NUM cana-5883 204 29 1297.https://doi.org/10.48550/arxiv.astro-ph/0105252 1297.https://doi.org/10.48550/arxiv.astro-ph/0105252 NUM cana-5883 204 30 4 4 NUM cana-5883 204 31 . . PUNCT cana-5883 205 1 jimenez jimenez PROPN cana-5883 205 2 , , PUNCT cana-5883 205 3 r. r. PROPN cana-5883 205 4 , , PUNCT cana-5883 205 5 stern stern ADJ cana-5883 205 6 , , PUNCT cana-5883 205 7 d. d. PROPN cana-5883 205 8 , , PUNCT cana-5883 205 9 verde verde PROPN cana-5883 205 10 , , PUNCT cana-5883 205 11 l. l. PROPN cana-5883 205 12 ,kamionkowski ,kamionkowski PROPN cana-5883 205 13 , , PUNCT cana-5883 205 14 m. m. NOUN cana-5883 205 15 , , PUNCT cana-5883 205 16 stanford stanford PROPN cana-5883 205 17 , , PUNCT cana-5883 205 18 sa sa PROPN cana-5883 205 19 . . PROPN cana-5883 205 20 , , PUNCT cana-5883 205 21 2010 2010 NUM cana-5883 205 22 . . PUNCT cana-5883 206 1 cosmic cosmic ADJ cana-5883 206 2 chronometers chronometer NOUN cana-5883 206 3 : : PUNCT cana-5883 206 4 constraining constrain VERB cana-5883 206 5 the the DET cana-5883 206 6 equation equation NOUN cana-5883 206 7 of of ADP cana-5883 206 8 state state NOUN cana-5883 206 9 of of ADP cana-5883 206 10 dark dark ADJ cana-5883 206 11 energy energy NOUN cana-5883 206 12 . . PUNCT cana-5883 207 1 i i PRON cana-5883 207 2 : : PUNCT cana-5883 207 3 h h PROPN cana-5883 207 4 ( ( PUNCT cana-5883 207 5 z z NOUN cana-5883 207 6 ) ) PUNCT cana-5883 207 7 measurements measurement NOUN cana-5883 207 8 , , PUNCT cana-5883 207 9 journal journal NOUN cana-5883 207 10 of of ADP cana-5883 207 11 cosmology cosmology PROPN cana-5883 207 12 and and CCONJ cana-5883 207 13 astroparticle astroparticle PROPN cana-5883 207 14 physics,(02),008 physics,(02),008 PROPN cana-5883 207 15 , , PUNCT cana-5883 207 16 http://dx.doi.org/10.1088/14757516/2010/02/008 http://dx.doi.org/10.1088/14757516/2010/02/008 NOUN cana-5883 207 17 5 5 NUM cana-5883 207 18 . . PUNCT cana-5883 208 1 peebles peeble NOUN cana-5883 208 2 p p PROPN cana-5883 208 3 j j PROPN cana-5883 208 4 e e PROPN cana-5883 208 5 , , PUNCT cana-5883 208 6 ratra ratra PROPN cana-5883 208 7 b b PROPN cana-5883 208 8 2003,the 2003,the DET cana-5883 208 9 cosmological cosmological ADJ cana-5883 208 10 constant constant ADJ cana-5883 208 11 and and CCONJ cana-5883 208 12 dark dark ADJ cana-5883 208 13 energy energy NOUN cana-5883 208 14 , , PUNCT cana-5883 208 15 rev rev PROPN cana-5883 208 16 . . PROPN cana-5883 208 17 modern modern ADJ cana-5883 208 18 physics physic NOUN cana-5883 208 19 75 75 NUM cana-5883 208 20 559-606.https://doi.org/10.48550/arxiv.astro-ph/0207347 559-606.https://doi.org/10.48550/arxiv.astro-ph/0207347 NUM cana-5883 208 21 6 6 NUM cana-5883 208 22 . . PUNCT cana-5883 209 1 sahni sahni PROPN cana-5883 209 2 v v PROPN cana-5883 209 3 , , PUNCT cana-5883 209 4 starobinsky starobinsky DET cana-5883 209 5 a a DET cana-5883 209 6 2000 2000 NUM cana-5883 209 7 , , PUNCT cana-5883 209 8 the the DET cana-5883 209 9 case case NOUN cana-5883 209 10 for for ADP cana-5883 209 11 a a DET cana-5883 209 12 positive positive ADJ cana-5883 209 13 cosmological cosmological ADJ cana-5883 209 14 lambda lambda ADJ cana-5883 209 15 - - PUNCT cana-5883 209 16 term term NOUN cana-5883 209 17 , , PUNCT cana-5883 209 18 international international ADJ cana-5883 209 19 journal journal NOUN cana-5883 209 20 of of ADP cana-5883 209 21 modern modern ADJ cana-5883 209 22 physics physics NOUN cana-5883 209 23 d d PROPN cana-5883 209 24 9 9 NUM cana-5883 209 25 373-443.https://doi.org/10.48550/arxiv.astroph/9904398 373-443.https://doi.org/10.48550/arxiv.astroph/9904398 NUM cana-5883 209 26 7.bento 7.bento NUM cana-5883 209 27 , , PUNCT cana-5883 209 28 m.c m.c PROPN cana-5883 209 29 . . PROPN cana-5883 209 30 , , PUNCT cana-5883 209 31 bertolami bertolami PROPN cana-5883 209 32 , , PUNCT cana-5883 209 33 o. o. PROPN cana-5883 209 34 and and CCONJ cana-5883 209 35 sen sen PROPN cana-5883 209 36 , , PUNCT cana-5883 209 37 a.a a.a PROPN cana-5883 209 38 . . PROPN cana-5883 209 39 , , PUNCT cana-5883 209 40 2002 2002 NUM cana-5883 209 41 . . PUNCT cana-5883 210 1 generalized generalize VERB cana-5883 210 2 chaplygin chaplygin NOUN cana-5883 210 3 gas gas NOUN cana-5883 210 4 , , PUNCT cana-5883 210 5 accelerated accelerate VERB cana-5883 210 6 expansion expansion NOUN cana-5883 210 7 , , PUNCT cana-5883 210 8 and and CCONJ cana-5883 210 9 dark dark ADJ cana-5883 210 10 - - PUNCT cana-5883 210 11 energy energy NOUN cana-5883 210 12 - - PUNCT cana-5883 210 13 matter matter NOUN cana-5883 210 14 unification unification NOUN cana-5883 210 15 , , PUNCT cana-5883 210 16 phys phy NOUN cana-5883 210 17 . . PUNCT cana-5883 211 1 rev rev PROPN cana-5883 211 2 . . PROPN cana-5883 211 3 d66(4 d66(4 PROPN cana-5883 211 4 ) ) PUNCT cana-5883 211 5 043507 043507 NUM cana-5883 211 6 . . PUNCT cana-5883 212 1 https://doi.org/10.1103/physrevd.66.043507 https://doi.org/10.1103/physrevd.66.043507 PROPN cana-5883 212 2 8.padmanabhan 8.padmanabhan NUM cana-5883 212 3 , , PUNCT cana-5883 212 4 t. t. NOUN cana-5883 212 5 and and CCONJ cana-5883 212 6 chaudhury chaudhury PROPN cana-5883 212 7 , , PUNCT cana-5883 212 8 t.r t.r PROPN cana-5883 212 9 . . PROPN cana-5883 212 10 ,2002 ,2002 PUNCT cana-5883 212 11 . . PUNCT cana-5883 213 1 can can AUX cana-5883 213 2 the the DET cana-5883 213 3 clustered clustered ADJ cana-5883 213 4 dark dark ADJ cana-5883 213 5 matter matter NOUN cana-5883 213 6 and and CCONJ cana-5883 213 7 the the DET cana-5883 213 8 smooth smooth ADJ cana-5883 213 9 dark dark ADJ cana-5883 213 10 energyarise energyarise NOUN cana-5883 213 11 from from ADP cana-5883 213 12 the the DET cana-5883 213 13 same same ADJ cana-5883 213 14 scalar scalar ADJ cana-5883 213 15 field?,phys field?,phy NOUN cana-5883 213 16 . . PUNCT cana-5883 214 1 rev rev PROPN cana-5883 214 2 . . PUNCT cana-5883 214 3 d66081301(r).https://doi.org/10.1103 d66081301(r).https://doi.org/10.1103 PROPN cana-5883 214 4 / / SYM cana-5883 214 5 physrevd.66.081301 physrevd.66.081301 NOUN cana-5883 214 6 9.martin 9.martin NUM cana-5883 214 7 , , PUNCT cana-5883 214 8 j. j. PROPN cana-5883 214 9 , , PUNCT cana-5883 214 10 2008 2008 NUM cana-5883 214 11 . . PUNCT cana-5883 215 1 quintessence quintessence NOUN cana-5883 215 2 : : PUNCT cana-5883 215 3 a a DET cana-5883 215 4 mini mini NOUN cana-5883 215 5 - - NOUN cana-5883 215 6 review review NOUN cana-5883 215 7 , , PUNCT cana-5883 215 8 mod mod PROPN cana-5883 215 9 . . PUNCT cana-5883 216 1 phys phys PROPN cana-5883 216 2 . . PUNCT cana-5883 217 1 lett lett PROPN cana-5883 217 2 . . PUNCT cana-5883 218 1 a a DET cana-5883 218 2 , , PUNCT cana-5883 218 3 23(17 23(17 NUM cana-5883 218 4 ) ) PUNCT cana-5883 219 1 1252.https://doi.org/10.48550/arxiv.0803.4076 1252.https://doi.org/10.48550/arxiv.0803.4076 PROPN cana-5883 219 2 10.nojiri 10.nojiri NUM cana-5883 219 3 s. s. PROPN cana-5883 219 4 , , PUNCT cana-5883 219 5 odintsov odintsov PROPN cana-5883 219 6 s. s. PROPN cana-5883 219 7 d. d. PROPN cana-5883 219 8 , , PUNCT cana-5883 219 9 sami sami PROPN cana-5883 219 10 , , PUNCT cana-5883 219 11 m. m. NOUN cana-5883 219 12 ,2006 ,2006 PUNCT cana-5883 219 13 .dark .dark PRON cana-5883 219 14 energy energy NOUN cana-5883 219 15 cosmology cosmology NOUN cana-5883 219 16 from from ADP cana-5883 219 17 higher high ADJ cana-5883 219 18 - - PUNCT cana-5883 219 19 order order NOUN cana-5883 219 20 , , PUNCT cana-5883 219 21 stringinspired stringinspired ADJ cana-5883 219 22 gravity gravity NOUN cana-5883 219 23 , , PUNCT cana-5883 219 24 and and CCONJ cana-5883 219 25 its its PRON cana-5883 219 26 reconstruction reconstruction NOUN cana-5883 219 27 , , PUNCT cana-5883 219 28 phys phy NOUN cana-5883 219 29 . . PUNCT cana-5883 220 1 rev rev PROPN cana-5883 220 2 . . PUNCT cana-5883 221 1 d d X cana-5883 221 2 74 74 NUM cana-5883 221 3 046004.https://doi.org/10.1103/physrevd.74.046004 046004.https://doi.org/10.1103/physrevd.74.046004 PROPN cana-5883 221 4 11 11 NUM cana-5883 221 5 . . PUNCT cana-5883 222 1 chiba chiba PROPN cana-5883 222 2 t t PROPN cana-5883 222 3 , , PUNCT cana-5883 222 4 okabe okabe PROPN cana-5883 222 5 t t PROPN cana-5883 222 6 , , PUNCT cana-5883 222 7 yamaguchi yamaguchi PROPN cana-5883 222 8 m. m. PROPN cana-5883 222 9 , , PUNCT cana-5883 222 10 2000.kinetically 2000.kinetically ADV cana-5883 222 11 driven drive VERB cana-5883 222 12 quintessence quintessence NOUN cana-5883 222 13 , , PUNCT cana-5883 222 14 phys phy NOUN cana-5883 222 15 . . PUNCT cana-5883 223 1 rev rev PROPN cana-5883 223 2 . . PUNCT cana-5883 224 1 d d X cana-5883 224 2 62 62 NUM cana-5883 225 1 023511.https://doi.org/10.1103/physrevd.62.023511 023511.https://doi.org/10.1103/physrevd.62.023511 NOUN cana-5883 226 1 12.singh 12.singh X cana-5883 226 2 g g PROPN cana-5883 226 3 p p X cana-5883 226 4 , , PUNCT cana-5883 226 5 kotambkar kotambkar PROPN cana-5883 226 6 s s PART cana-5883 226 7 and and CCONJ cana-5883 226 8 pradhan pradhan PROPN cana-5883 226 9 a a DET cana-5883 226 10 .,2006.cosmological .,2006.cosmological ADJ cana-5883 226 11 models model NOUN cana-5883 226 12 with with ADP cana-5883 226 13 a a DET cana-5883 226 14 variable variable ADJ cana-5883 226 15 Ξ» Ξ» NOUN cana-5883 226 16 term term NOUN cana-5883 226 17 in in ADP cana-5883 226 18 higher high ADJ cana-5883 226 19 dimensional dimensional ADJ cana-5883 226 20 space space NOUN cana-5883 226 21 - - PUNCT cana-5883 226 22 time time NOUN cana-5883 226 23 fizika fizika PROPN cana-5883 226 24 b b PROPN cana-5883 226 25 ( ( PUNCT cana-5883 226 26 zagreb zagreb PROPN cana-5883 226 27 ) ) PUNCT cana-5883 226 28 15 15 NUM cana-5883 226 29 23 23 NUM cana-5883 226 30 - - SYM cana-5883 226 31 26 26 NUM cana-5883 226 32 . . PUNCT cana-5883 227 1 13.buchdahl 13.buchdahl NUM cana-5883 227 2 , , PUNCT cana-5883 227 3 h.a h.a PROPN cana-5883 227 4 . . PROPN cana-5883 227 5 ,1970 ,1970 PROPN cana-5883 227 6 . . PUNCT cana-5883 228 1 non non ADJ cana-5883 228 2 - - ADJ cana-5883 228 3 linear linear ADJ cana-5883 228 4 lagrangians lagrangian NOUN cana-5883 228 5 and and CCONJ cana-5883 228 6 cosmological cosmological ADJ cana-5883 228 7 theory theory NOUN cana-5883 228 8 , , PUNCT cana-5883 228 9 not not PART cana-5883 228 10 . . PUNCT cana-5883 229 1 r. r. PROPN cana-5883 229 2 astron astron PROPN cana-5883 229 3 . . PUNCT cana-5883 230 1 soc.150.https://doi.org/10.1093/mnras/150.1.1 soc.150.https://doi.org/10.1093/mnras/150.1.1 NOUN cana-5883 230 2 14 14 NUM cana-5883 230 3 . . PUNCT cana-5883 231 1 starobinsky starobinsky PROPN cana-5883 231 2 , , PUNCT cana-5883 231 3 a.a a.a PROPN cana-5883 231 4 . . PROPN cana-5883 231 5 ,1980 ,1980 PROPN cana-5883 231 6 . . PUNCT cana-5883 232 1 a a DET cana-5883 232 2 new new ADJ cana-5883 232 3 type type NOUN cana-5883 232 4 of of ADP cana-5883 232 5 isotropic isotropic ADJ cana-5883 232 6 cosmological cosmological ADJ cana-5883 232 7 models model NOUN cana-5883 232 8 without without ADP cana-5883 232 9 singularity singularity NOUN cana-5883 232 10 , , PUNCT cana-5883 232 11 phys phy NOUN cana-5883 232 12 . . PUNCT cana-5883 233 1 lett lett PROPN cana-5883 233 2 . . PROPN cana-5883 234 1 , , PUNCT cana-5883 235 1 b b X cana-5883 235 2 91 91 NUM cana-5883 235 3 99.https://doi.org/10.1016/0370-2693(80)90670-x 99.https://doi.org/10.1016/0370-2693(80)90670-x NUM cana-5883 235 4 15 15 NUM cana-5883 235 5 . . PUNCT cana-5883 236 1 carroll carroll PROPN cana-5883 236 2 , , PUNCT cana-5883 236 3 s.m s.m PROPN cana-5883 236 4 . . PROPN cana-5883 236 5 , , PUNCT cana-5883 236 6 duwuri duwuri PROPN cana-5883 236 7 , , PUNCT cana-5883 236 8 v. v. ADV cana-5883 236 9 , , PUNCT cana-5883 236 10 trodden trodden ADJ cana-5883 236 11 , , PUNCT cana-5883 236 12 m. m. NOUN cana-5883 236 13 and and CCONJ cana-5883 236 14 turner turner PROPN cana-5883 236 15 , , PUNCT cana-5883 236 16 m.s m.s PROPN cana-5883 236 17 . . PROPN cana-5883 236 18 ,2004.is ,2004.is PUNCT cana-5883 237 1 cosmic cosmic ADJ cana-5883 237 2 speed speed NOUN cana-5883 237 3 - - PUNCT cana-5883 237 4 up up NOUN cana-5883 237 5 due due ADJ cana-5883 237 6 to to ADP cana-5883 237 7 new new ADJ cana-5883 237 8 gravitational gravitational ADJ cana-5883 237 9 physics?,phys physics?,phy NOUN cana-5883 237 10 . . PUNCT cana-5883 238 1 rev rev PROPN cana-5883 238 2 . . PROPN cana-5883 238 3 d70043528.https://doi.org/10.1103/physrevd.70.043528 d70043528.https://doi.org/10.1103/physrevd.70.043528 PROPN cana-5883 239 1 https://doi.org/10.1086/300499 https://doi.org/10.1086/300499 AUX cana-5883 239 2 https://doi.org/10.1086/307221 https://doi.org/10.1086/307221 X cana-5883 239 3 https://doi.org/10.48550/arxiv.astro-ph/0105252 https://doi.org/10.48550/arxiv.astro-ph/0105252 NOUN cana-5883 239 4 http://dx.doi.org/10.1088/1475-7516/2010/02/008 http://dx.doi.org/10.1088/1475-7516/2010/02/008 NOUN cana-5883 239 5 http://dx.doi.org/10.1088/1475-7516/2010/02/008 http://dx.doi.org/10.1088/1475-7516/2010/02/008 X cana-5883 239 6 https://doi.org/10.48550/arxiv.astro-ph/0207347 https://doi.org/10.48550/arxiv.astro-ph/0207347 ADJ cana-5883 239 7 https://doi.org/10.48550/arxiv.astro-ph/9904398 https://doi.org/10.48550/arxiv.astro-ph/9904398 NUM cana-5883 239 8 https://doi.org/10.48550/arxiv.astro-ph/9904398 https://doi.org/10.48550/arxiv.astro-ph/9904398 NUM cana-5883 239 9 https://doi.org/10.1103/physrevd.66.043507 https://doi.org/10.1103/physrevd.66.043507 VERB cana-5883 239 10 https://doi.org/10.1103/physrevd.66.081301 https://doi.org/10.1103/physrevd.66.081301 NOUN cana-5883 239 11 https://doi.org/10.48550/arxiv.0803.4076 https://doi.org/10.48550/arxiv.0803.4076 PROPN cana-5883 239 12 https://doi.org/10.1103/physrevd.74.046004 https://doi.org/10.1103/physrevd.74.046004 NOUN cana-5883 239 13 https://doi.org/10.1103/physrevd.62.023511 https://doi.org/10.1103/physrevd.62.023511 NOUN cana-5883 239 14 https://doi.org/10.1093/mnras/150.1.1 https://doi.org/10.1093/mnras/150.1.1 PROPN cana-5883 239 15 https://doi.org/10.1016/0370-2693(80)90670-x https://doi.org/10.1016/0370-2693(80)90670-x PROPN cana-5883 239 16 https://doi.org/10.1103/physrevd.70.043528 https://doi.org/10.1103/physrevd.70.043528 PROPN cana-5883 239 17 communications communication NOUN cana-5883 239 18 on on ADP cana-5883 239 19 applied apply VERB cana-5883 239 20 nonlinear nonlinear ADJ cana-5883 239 21 analysis analysis NOUN cana-5883 239 22 issn issn NOUN cana-5883 239 23 : : PUNCT cana-5883 239 24 1074 1074 NUM cana-5883 239 25 - - PUNCT cana-5883 239 26 133x 133x NUM cana-5883 239 27 vol vol NOUN cana-5883 239 28 32 32 NUM cana-5883 239 29 no no NOUN cana-5883 239 30 . . PUNCT cana-5883 240 1 2s 2s NUM cana-5883 240 2 ( ( PUNCT cana-5883 240 3 2025 2025 NUM cana-5883 240 4 ) ) PUNCT cana-5883 240 5 617 617 NUM cana-5883 240 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 240 7 16.chiba 16.chiba NUM cana-5883 240 8 , , PUNCT cana-5883 240 9 t. t. NOUN cana-5883 240 10 and and CCONJ cana-5883 240 11 erichcek erichcek NUM cana-5883 240 12 , , PUNCT cana-5883 240 13 a.l a.l PROPN cana-5883 240 14 . . PROPN cana-5883 240 15 ,2007.solar ,2007.solar PUNCT cana-5883 240 16 system system NOUN cana-5883 240 17 constraints constraint NOUN cana-5883 240 18 to to ADP cana-5883 240 19 general general ADJ cana-5883 240 20 f(r)gravity f(r)gravity NOUN cana-5883 240 21 , , PUNCT cana-5883 240 22 phys.rev.d75,124014.https://doi.org/10.1103 phys.rev.d75,124014.https://doi.org/10.1103 NOUN cana-5883 240 23 / / SYM cana-5883 240 24 physrevd.75.124014 physrevd.75.124014 NOUN cana-5883 240 25 17.aktaş 17.aktaş NUM cana-5883 240 26 , , PUNCT cana-5883 240 27 c. c. NOUN cana-5883 240 28 , , PUNCT cana-5883 240 29 aygΓΌn aygΓΌn NOUN cana-5883 240 30 , , PUNCT cana-5883 240 31 s. s. PROPN cana-5883 240 32 and and CCONJ cana-5883 240 33 yΔ±lmaz yΔ±lmaz PROPN cana-5883 240 34 , , PUNCT cana-5883 240 35 iΜ‡. iΜ‡. NOUN cana-5883 240 36 , , PUNCT cana-5883 240 37 2012 2012 NUM cana-5883 240 38 . . PUNCT cana-5883 241 1 behaviors behavior NOUN cana-5883 241 2 of of ADP cana-5883 241 3 dark dark ADJ cana-5883 241 4 energy energy NOUN cana-5883 241 5 and and CCONJ cana-5883 241 6 mesonic mesonic ADJ cana-5883 241 7 scalar scalar ADJ cana-5883 241 8 field field NOUN cana-5883 241 9 foranisotropic foranisotropic ADJ cana-5883 241 10 universe universe NOUN cana-5883 241 11 in in ADP cana-5883 241 12 f f PROPN cana-5883 241 13 ( ( PUNCT cana-5883 241 14 r r NOUN cana-5883 241 15 ) ) PUNCT cana-5883 241 16 gravity gravity NOUN cana-5883 241 17 , , PUNCT cana-5883 241 18 phys phy NOUN cana-5883 241 19 . . PUNCT cana-5883 242 1 lett lett PROPN cana-5883 242 2 . . PUNCT cana-5883 243 1 b707 b707 PROPN cana-5883 243 2 , , PUNCT cana-5883 243 3 237 237 NUM cana-5883 243 4 . . PUNCT cana-5883 244 1 doi doi NOUN cana-5883 244 2 : : PUNCT cana-5883 244 3 10.1016 10.1016 NUM cana-5883 244 4 / / SYM cana-5883 244 5 j.physletb.2011.12.043 j.physletb.2011.12.043 PROPN cana-5883 244 6 18.reddy 18.reddy NUM cana-5883 244 7 , , PUNCT cana-5883 244 8 d.r.k d.r.k PROPN cana-5883 244 9 , , PUNCT cana-5883 244 10 adhav adhav PROPN cana-5883 244 11 , , PUNCT cana-5883 244 12 k.s k.s PROPN cana-5883 244 13 . . PROPN cana-5883 244 14 and and CCONJ cana-5883 244 15 munde munde PROPN cana-5883 244 16 , , PUNCT cana-5883 244 17 s. s. PROPN cana-5883 244 18 l. l. PROPN cana-5883 244 19 ,2014.vacuum ,2014.vacuum PUNCT cana-5883 244 20 solutions solution NOUN cana-5883 244 21 of of ADP cana-5883 244 22 bianchi bianchi NOUN cana-5883 244 23 type type NOUN cana-5883 244 24 - - PUNCT cana-5883 244 25 i i PRON cana-5883 244 26 and and CCONJ cana-5883 244 27 v v NUM cana-5883 244 28 models model NOUN cana-5883 244 29 in in ADP cana-5883 244 30 f f PROPN cana-5883 244 31 ( ( PUNCT cana-5883 244 32 r r NOUN cana-5883 244 33 ) ) PUNCT cana-5883 244 34 gravity gravity NOUN cana-5883 244 35 with with ADP cana-5883 244 36 a a DET cana-5883 244 37 special special ADJ cana-5883 244 38 form form NOUN cana-5883 244 39 of of ADP cana-5883 244 40 deceleration deceleration NOUN cana-5883 244 41 parameter parameter NOUN cana-5883 244 42 , , PUNCT cana-5883 244 43 int int NOUN cana-5883 244 44 . . PUNCT cana-5883 245 1 j. j. PROPN cana-5883 245 2 sci sci PROPN cana-5883 245 3 . . PUNCT cana-5883 246 1 adv adv PROPN cana-5883 246 2 . . PUNCT cana-5883 246 3 tech tech NOUN cana-5883 246 4 . . PUNCT cana-5883 247 1 4 4 NUM cana-5883 247 2 , , PUNCT cana-5883 247 3 23 23 NUM cana-5883 247 4 . . PUNCT cana-5883 248 1 19.a.a 19.a.a NUM cana-5883 248 2 . . PUNCT cana-5883 249 1 starobinsky,2007 starobinsky,2007 NOUN cana-5883 249 2 . . PUNCT cana-5883 250 1 disappearing disappear VERB cana-5883 250 2 cosmological cosmological ADJ cana-5883 250 3 constant constant ADJ cana-5883 250 4 in in ADP cana-5883 250 5 f(r f(r NOUN cana-5883 250 6 ) ) PUNCT cana-5883 250 7 gravity gravity NOUN cana-5883 250 8 , , PUNCT cana-5883 250 9 jetp jetp PROPN cana-5883 250 10 lett lett PROPN cana-5883 250 11 . . PUNCT cana-5883 250 12 86,157.https://doi.org/10.48550 86,157.https://doi.org/10.48550 NUM cana-5883 250 13 / / SYM cana-5883 250 14 arxiv.0706.2041 arxiv.0706.2041 NOUN cana-5883 250 15 20.nojiri 20.nojiri NUM cana-5883 250 16 , , PUNCT cana-5883 250 17 s. s. PROPN cana-5883 250 18 , , PUNCT cana-5883 250 19 and and CCONJ cana-5883 250 20 odintsov odintsov PROPN cana-5883 250 21 , , PUNCT cana-5883 250 22 s.d s.d PROPN cana-5883 250 23 . . PROPN cana-5883 250 24 , , PUNCT cana-5883 250 25 2007 2007 NUM cana-5883 250 26 . . PUNCT cana-5883 251 1 introduction introduction NOUN cana-5883 251 2 to to ADP cana-5883 251 3 modified modify VERB cana-5883 251 4 gravity gravity NOUN cana-5883 251 5 and and CCONJ cana-5883 251 6 gravitational gravitational ADJ cana-5883 251 7 alternative alternative NOUN cana-5883 251 8 for for ADP cana-5883 251 9 dark dark ADJ cana-5883 251 10 energy energy NOUN cana-5883 251 11 , , PUNCT cana-5883 251 12 int int NOUN cana-5883 251 13 . . PUNCT cana-5883 252 1 j. j. PROPN cana-5883 252 2 geom geom PROPN cana-5883 252 3 . . PUNCT cana-5883 253 1 method method PROPN cana-5883 253 2 mod mod PROPN cana-5883 253 3 . . PUNCT cana-5883 254 1 phys phys PROPN cana-5883 254 2 . . PUNCT cana-5883 255 1 4115.https://doi.org/10.1142/s0219887807001928 4115.https://doi.org/10.1142/s0219887807001928 NUM cana-5883 255 2 21 21 NUM cana-5883 255 3 . . PUNCT cana-5883 256 1 nojiri nojiri ADV cana-5883 256 2 , , PUNCT cana-5883 256 3 s. s. PROPN cana-5883 256 4 and and CCONJ cana-5883 256 5 odintsov odintsov PROPN cana-5883 256 6 , , PUNCT cana-5883 256 7 s.d.2011 s.d.2011 PROPN cana-5883 256 8 , , PUNCT cana-5883 256 9 unified unified ADJ cana-5883 256 10 cosmic cosmic ADJ cana-5883 256 11 history history NOUN cana-5883 256 12 in in ADP cana-5883 256 13 modified modified ADJ cana-5883 256 14 gravity gravity NOUN cana-5883 256 15 : : PUNCT cana-5883 256 16 from from ADP cana-5883 256 17 theory theory NOUN cana-5883 256 18 to to ADP cana-5883 256 19 lorentz lorentz PROPN cana-5883 256 20 non non ADJ cana-5883 256 21 - - ADJ cana-5883 256 22 invariant invariant ADJ cana-5883 256 23 models model NOUN cana-5883 256 24 , , PUNCT cana-5883 256 25 phys phy NOUN cana-5883 256 26 . . PUNCT cana-5883 257 1 rep rep PROPN cana-5883 257 2 . . PROPN cana-5883 257 3 505 505 NUM cana-5883 257 4 , , PUNCT cana-5883 257 5 59.https://doi.org/10.1016/j.physrep.2011.04.001 59.https://doi.org/10.1016/j.physrep.2011.04.001 NUM cana-5883 257 6 22.nojiri 22.nojiri NUM cana-5883 257 7 , , PUNCT cana-5883 257 8 s. s. PROPN cana-5883 257 9 and and CCONJ cana-5883 257 10 odintsov odintsov PROPN cana-5883 257 11 , , PUNCT cana-5883 257 12 s.d s.d PROPN cana-5883 257 13 . . PROPN cana-5883 257 14 2003 2003 NUM cana-5883 257 15 . . PUNCT cana-5883 258 1 modified modify VERB cana-5883 258 2 gravity gravity NOUN cana-5883 258 3 with with ADP cana-5883 258 4 negative negative ADJ cana-5883 258 5 and and CCONJ cana-5883 258 6 positive positive ADJ cana-5883 258 7 powers power NOUN cana-5883 258 8 of of ADP cana-5883 258 9 curvature curvature NOUN cana-5883 258 10 : : PUNCT cana-5883 258 11 unification unification NOUN cana-5883 258 12 of of ADP cana-5883 258 13 inflation inflation NOUN cana-5883 258 14 and and CCONJ cana-5883 258 15 cosmic cosmic ADJ cana-5883 258 16 acceleration acceleration NOUN cana-5883 258 17 , , PUNCT cana-5883 258 18 phys phy NOUN cana-5883 258 19 . . PUNCT cana-5883 259 1 rev rev PROPN cana-5883 259 2 . . PROPN cana-5883 259 3 d68,123512.https://doi.org/10.1103 d68,123512.https://doi.org/10.1103 PROPN cana-5883 259 4 / / SYM cana-5883 259 5 physrevd.68.123512 physrevd.68.123512 ADJ cana-5883 259 6 23d 23d NOUN cana-5883 259 7 . . PUNCT cana-5883 260 1 n.spergelet n.spergelet PROPN cana-5883 260 2 al al PROPN cana-5883 260 3 . . PROPN cana-5883 260 4 ,2003.first ,2003.first PUNCT cana-5883 260 5 year year PROPN cana-5883 260 6 wilkinson wilkinson PROPN cana-5883 260 7 microwave microwave PROPN cana-5883 260 8 anisotropy anisotropy NOUN cana-5883 260 9 probe probe NOUN cana-5883 260 10 ( ( PUNCT cana-5883 260 11 wmap wmap ADJ cana-5883 260 12 ) ) PUNCT cana-5883 260 13 observations observation NOUN cana-5883 260 14 : : PUNCT cana-5883 260 15 determination determination NOUN cana-5883 260 16 of of ADP cana-5883 260 17 cosmological cosmological ADJ cana-5883 260 18 parameters parameter NOUN cana-5883 260 19 , , PUNCT cana-5883 260 20 astrophys astrophy NOUN cana-5883 260 21 . . PUNCT cana-5883 261 1 j. j. PROPN cana-5883 261 2 suppl suppl PROPN cana-5883 261 3 . . PUNCT cana-5883 262 1 148175 148175 NUM cana-5883 262 2 . . PUNCT cana-5883 263 1 10.1086/377226 10.1086/377226 NUM cana-5883 263 2 24 24 NUM cana-5883 263 3 . . PUNCT cana-5883 263 4 misner misner NOUN cana-5883 263 5 , , PUNCT cana-5883 263 6 c.w c.w PROPN cana-5883 263 7 . . PROPN cana-5883 263 8 , , PUNCT cana-5883 263 9 1968 1968 NUM cana-5883 263 10 . . PUNCT cana-5883 264 1 the the DET cana-5883 264 2 isotropy isotropy NOUN cana-5883 264 3 of of ADP cana-5883 264 4 the the DET cana-5883 264 5 universe universe NOUN cana-5883 264 6 , , PUNCT cana-5883 264 7 astrophysical astrophysical ADJ cana-5883 264 8 journal,151,431 journal,151,431 NOUN cana-5883 264 9 . . PUNCT cana-5883 265 1 https://ui.adsabs.harvard.edu/link_gateway/1968apj...151..431m/doi:10.1086/149448 https://ui.adsabs.harvard.edu/link_gateway/1968apj...151..431m/doi:10.1086/149448 NOUN cana-5883 265 2 25 25 NUM cana-5883 265 3 . . PUNCT cana-5883 266 1 gibbons gibbon NOUN cana-5883 266 2 , , PUNCT cana-5883 266 3 g.w g.w PROPN cana-5883 266 4 . . PROPN cana-5883 266 5 and and CCONJ cana-5883 266 6 hawking hawking PROPN cana-5883 266 7 , , PUNCT cana-5883 266 8 s.w s.w PROPN cana-5883 266 9 . . PROPN cana-5883 266 10 , , PUNCT cana-5883 266 11 1977.cosmological 1977.cosmological ADJ cana-5883 266 12 event event NOUN cana-5883 266 13 horizons horizon NOUN cana-5883 266 14 , , PUNCT cana-5883 266 15 thermodynamics thermodynamic NOUN cana-5883 266 16 , , PUNCT cana-5883 266 17 and and CCONJ cana-5883 266 18 particle particle NOUN cana-5883 266 19 creation creation NOUN cana-5883 266 20 , , PUNCT cana-5883 266 21 phys phy NOUN cana-5883 266 22 . . PUNCT cana-5883 267 1 rev rev PROPN cana-5883 267 2 . . PROPN cana-5883 267 3 d15 d15 PROPN cana-5883 267 4 2738.https://doi.org/10.1103/physrevd.15.2738 2738.https://doi.org/10.1103/physrevd.15.2738 PROPN cana-5883 267 5 26 26 NUM cana-5883 267 6 . . PUNCT cana-5883 268 1 harko harko ADJ cana-5883 268 2 , , PUNCT cana-5883 268 3 t. t. PROPN cana-5883 268 4 , , PUNCT cana-5883 268 5 lobo lobo PROPN cana-5883 268 6 , , PUNCT cana-5883 268 7 f. f. PROPN cana-5883 268 8 s. s. PROPN cana-5883 268 9 , , PUNCT cana-5883 268 10 nojiri nojiri ADV cana-5883 268 11 , , PUNCT cana-5883 268 12 s. s. PROPN cana-5883 268 13 i. i. PROPN cana-5883 268 14 and and CCONJ cana-5883 268 15 odintsov odintsov PROPN cana-5883 268 16 , , PUNCT cana-5883 268 17 s. s. PROPN cana-5883 268 18 d. d. PROPN cana-5883 268 19 2011 2011 NUM cana-5883 268 20 . . PUNCT cana-5883 269 1 β€˜ ' PUNCT cana-5883 269 2 β€˜ ' PUNCT cana-5883 269 3 f(r f(r X cana-5883 269 4 , , PUNCT cana-5883 269 5 t t NOUN cana-5883 269 6 ) ) PUNCT cana-5883 269 7 gravity gravity NOUN cana-5883 269 8 , , PUNCT cana-5883 269 9 ’’ ’' PUNCT cana-5883 269 10 phys phy NOUN cana-5883 269 11 . . PUNCT cana-5883 270 1 rev rev PROPN cana-5883 270 2 . . PROPN cana-5883 271 1 d d X cana-5883 271 2 , , PUNCT cana-5883 271 3 vol vol NOUN cana-5883 271 4 . . PROPN cana-5883 271 5 84 84 NUM cana-5883 271 6 , , PUNCT cana-5883 271 7 p. p. NOUN cana-5883 271 8 024020,.https://doi.org/10.1103 024020,.https://doi.org/10.1103 NUM cana-5883 271 9 / / SYM cana-5883 271 10 physrevd.84.024020 physrevd.84.024020 PROPN cana-5883 271 11 27 27 NUM cana-5883 271 12 . . PUNCT cana-5883 272 1 adhav adhav PROPN cana-5883 272 2 , , PUNCT cana-5883 272 3 k. k. PROPN cana-5883 272 4 s. s. PROPN cana-5883 272 5 , , PUNCT cana-5883 272 6 2012 2012 NUM cana-5883 272 7 . . PUNCT cana-5883 273 1 lrs lrs PROPN cana-5883 273 2 bianchi bianchi PROPN cana-5883 273 3 type type PROPN cana-5883 273 4 - - PUNCT cana-5883 273 5 i i PRON cana-5883 273 6 cosmological cosmological ADJ cana-5883 273 7 model model NOUN cana-5883 273 8 in in ADP cana-5883 273 9 f(r f(r PROPN cana-5883 273 10 , , PUNCT cana-5883 273 11 t t NOUN cana-5883 273 12 ) ) PUNCT cana-5883 273 13 theory theory NOUN cana-5883 273 14 of of ADP cana-5883 273 15 gravity gravity NOUN cana-5883 273 16 , , PUNCT cana-5883 273 17 astrophys astrophy NOUN cana-5883 273 18 space space NOUN cana-5883 273 19 sci339(2012)365.https://ui.adsabs.harvard.edu sci339(2012)365.https://ui.adsabs.harvard.edu NOUN cana-5883 273 20 / / SYM cana-5883 273 21 link_gateway/2012ap&ss.339 link_gateway/2012ap&ss.339 PROPN cana-5883 273 22 .. .. SYM cana-5883 273 23 365a 365a PROPN cana-5883 273 24 / / SYM cana-5883 273 25 doi doi NOUN cana-5883 273 26 : : PUNCT cana-5883 273 27 10.1007 10.1007 NUM cana-5883 273 28 / / SYM cana-5883 273 29 s10509 s10509 NOUN cana-5883 273 30 - - PUNCT cana-5883 273 31 011 011 NUM cana-5883 273 32 - - PUNCT cana-5883 273 33 0963 0963 NUM cana-5883 273 34 - - SYM cana-5883 273 35 8 8 NUM cana-5883 273 36 28 28 NUM cana-5883 273 37 . . PUNCT cana-5883 274 1 sahoo sahoo PROPN cana-5883 274 2 , , PUNCT cana-5883 274 3 p. p. PROPN cana-5883 274 4 k. k. PROPN cana-5883 274 5 and and CCONJ cana-5883 274 6 sivakumar sivakumar PROPN cana-5883 274 7 , , PUNCT cana-5883 274 8 m. m. NOUN cana-5883 274 9 , , PUNCT cana-5883 274 10 2015 2015 NUM cana-5883 274 11 . . PUNCT cana-5883 275 1 lrs lrs PROPN cana-5883 275 2 bianchi bianchi PROPN cana-5883 275 3 type type PROPN cana-5883 275 4 - - PUNCT cana-5883 275 5 i i PRON cana-5883 275 6 cosmological cosmological ADJ cana-5883 275 7 model model NOUN cana-5883 275 8 in in ADP cana-5883 275 9 f(r f(r PROPN cana-5883 275 10 , , PUNCT cana-5883 275 11 t t NOUN cana-5883 275 12 ) ) PUNCT cana-5883 275 13 theory theory NOUN cana-5883 275 14 of of ADP cana-5883 275 15 gravity gravity NOUN cana-5883 275 16 with with ADP cana-5883 275 17 Ξ»(t Ξ»(t NOUN cana-5883 275 18 ) ) PUNCT cana-5883 275 19 , , PUNCT cana-5883 275 20 astrophys astrophy NOUN cana-5883 275 21 space space NOUN cana-5883 275 22 sci35760.https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/ sci35760.https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/ PROPN cana-5883 275 23 s10509 s10509 PROPN cana-5883 275 24 - - PUNCT cana-5883 275 25 015 015 NUM cana-5883 275 26 - - PUNCT cana-5883 275 27 2264 2264 NUM cana-5883 275 28 - - SYM cana-5883 275 29 0 0 NUM cana-5883 275 30 29 29 NUM cana-5883 275 31 . . PUNCT cana-5883 276 1 shamir shamir PROPN cana-5883 276 2 , , PUNCT cana-5883 276 3 m.f m.f PROPN cana-5883 276 4 . . PROPN cana-5883 276 5 , , PUNCT cana-5883 276 6 2014 2014 NUM cana-5883 276 7 . . PUNCT cana-5883 277 1 exact exact ADJ cana-5883 277 2 solutions solution NOUN cana-5883 277 3 of of ADP cana-5883 277 4 bianchi bianchi NOUN cana-5883 277 5 type type NOUN cana-5883 277 6 v v NOUN cana-5883 277 7 spacetime spacetime NOUN cana-5883 277 8 in in ADP cana-5883 277 9 f f PROPN cana-5883 277 10 ( ( PUNCT cana-5883 277 11 r r PROPN cana-5883 277 12 , , PUNCT cana-5883 277 13 t t NOUN cana-5883 277 14 ) ) PUNCT cana-5883 277 15 gravity gravity NOUN cana-5883 277 16 , , PUNCT cana-5883 277 17 int int PROPN cana-5883 277 18 j j PROPN cana-5883 277 19 theor theor PROPN cana-5883 277 20 phys phy NOUN cana-5883 277 21 541304-1315.http://dx.doi.org/10.1007/s10773-014-2328-x 541304-1315.http://dx.doi.org/10.1007/s10773-014-2328-x NUM cana-5883 277 22 30 30 NUM cana-5883 277 23 . . PUNCT cana-5883 278 1 chaubey chaubey PROPN cana-5883 278 2 , , PUNCT cana-5883 278 3 r. r. PROPN cana-5883 278 4 shukla shukla PROPN cana-5883 278 5 , , PUNCT cana-5883 278 6 a. a. PROPN cana-5883 278 7 k. k. PROPN cana-5883 278 8 ,raushan ,raushan PROPN cana-5883 278 9 , , PUNCT cana-5883 278 10 r r NOUN cana-5883 278 11 .and .and PUNCT cana-5883 278 12 singh singh PROPN cana-5883 278 13 , , PUNCT cana-5883 278 14 t. t. PROPN cana-5883 278 15 ,2016 ,2016 PUNCT cana-5883 278 16 . . PUNCT cana-5883 279 1 the the DET cana-5883 279 2 general general ADJ cana-5883 279 3 class class NOUN cana-5883 279 4 of of ADP cana-5883 279 5 bianchi bianchi NOUN cana-5883 279 6 cosmological cosmological ADJ cana-5883 279 7 models model NOUN cana-5883 279 8 in in ADP cana-5883 279 9 f f PROPN cana-5883 279 10 ( ( PUNCT cana-5883 279 11 r r NOUN cana-5883 279 12 , , PUNCT cana-5883 279 13 t t NOUN cana-5883 279 14 ) ) PUNCT cana-5883 279 15 gravity gravity NOUN cana-5883 279 16 with with ADP cana-5883 279 17 dark dark ADJ cana-5883 279 18 energy energy NOUN cana-5883 279 19 in in ADP cana-5883 279 20 viscous viscous ADJ cana-5883 279 21 cosmology cosmology NOUN cana-5883 279 22 , , PUNCT cana-5883 279 23 indian indian PROPN cana-5883 279 24 j. j. PROPN cana-5883 279 25 phys90,233.doihttps://doi.org/10.1007 phys90,233.doihttps://doi.org/10.1007 PROPN cana-5883 279 26 / / SYM cana-5883 279 27 s12648 s12648 PROPN cana-5883 279 28 - - PUNCT cana-5883 279 29 015 015 NUM cana-5883 279 30 - - PUNCT cana-5883 279 31 0749 0749 NUM cana-5883 279 32 - - PUNCT cana-5883 279 33 x x NOUN cana-5883 279 34 https://doi.org/10.1103/physrevd.75.124014 https://doi.org/10.1103/physrevd.75.124014 NOUN cana-5883 279 35 http://dx.doi.org/10.1016/j.physletb.2011.12.043 http://dx.doi.org/10.1016/j.physletb.2011.12.043 PROPN cana-5883 279 36 https://doi.org/10.48550/arxiv.0706.2041 https://doi.org/10.48550/arxiv.0706.2041 PROPN cana-5883 279 37 https://doi.org/10.1142/s0219887807001928 https://doi.org/10.1142/s0219887807001928 NUM cana-5883 279 38 https://doi.org/10.1016/j.physrep.2011.04.001 https://doi.org/10.1016/j.physrep.2011.04.001 VERB cana-5883 279 39 https://doi.org/10.1103/physrevd.68.123512 https://doi.org/10.1103/physrevd.68.123512 NOUN cana-5883 279 40 https://ui.adsabs.harvard.edu/link_gateway/1968apj...151..431m/doi:10.1086/149448 https://ui.adsabs.harvard.edu/link_gateway/1968apj...151..431m/doi:10.1086/149448 NOUN cana-5883 279 41 https://doi.org/10.1103/physrevd.15.2738 https://doi.org/10.1103/physrevd.15.2738 NOUN cana-5883 279 42 https://doi.org/10.1103/physrevd.84.024020 https://doi.org/10.1103/physrevd.84.024020 VERB cana-5883 279 43 https://ui.adsabs.harvard.edu/link_gateway/2012ap&ss.339..365a/doi:10.1007/s10509-011-0963-8 https://ui.adsabs.harvard.edu/link_gateway/2012ap&ss.339..365a/doi:10.1007/s10509-011-0963-8 NUM cana-5883 279 44 https://ui.adsabs.harvard.edu/link_gateway/2012ap&ss.339..365a/doi:10.1007/s10509-011-0963-8 https://ui.adsabs.harvard.edu/link_gateway/2012ap&ss.339..365a/doi:10.1007/s10509-011-0963-8 NUM cana-5883 280 1 https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/s10509-015-2264-0 https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/s10509-015-2264-0 NOUN cana-5883 280 2 https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/s10509-015-2264-0 https://ui.adsabs.harvard.edu/link_gateway/2015ap&ss.357...60s/doi:10.1007/s10509-015-2264-0 NOUN cana-5883 280 3 http://dx.doi.org/10.1007/s10773-014-2328-x http://dx.doi.org/10.1007/s10773-014-2328-x PROPN cana-5883 280 4 communications communication NOUN cana-5883 280 5 on on ADP cana-5883 280 6 applied apply VERB cana-5883 280 7 nonlinear nonlinear ADJ cana-5883 280 8 analysis analysis NOUN cana-5883 280 9 issn issn NOUN cana-5883 280 10 : : PUNCT cana-5883 280 11 1074 1074 NUM cana-5883 280 12 - - PUNCT cana-5883 280 13 133x 133x NUM cana-5883 280 14 vol vol NOUN cana-5883 280 15 32 32 NUM cana-5883 280 16 no no NOUN cana-5883 280 17 . . PUNCT cana-5883 281 1 2s 2s NUM cana-5883 281 2 ( ( PUNCT cana-5883 281 3 2025 2025 NUM cana-5883 281 4 ) ) PUNCT cana-5883 281 5 618 618 NUM cana-5883 281 6 https://internationalpubls.com https://internationalpubls.com X cana-5883 281 7 31.bishi 31.bishi PROPN cana-5883 281 8 , , PUNCT cana-5883 281 9 b. b. PROPN cana-5883 281 10 k. k. PROPN cana-5883 281 11 ,et ,et PROPN cana-5883 282 1 al al PROPN cana-5883 282 2 . . PROPN cana-5883 282 3 ,2021.cosmology ,2021.cosmology PUNCT cana-5883 282 4 in in ADP cana-5883 282 5 f(r f(r PROPN cana-5883 282 6 , , PUNCT cana-5883 282 7 t t NOUN cana-5883 282 8 ) ) PUNCT cana-5883 282 9 gravity gravity NOUN cana-5883 282 10 with with ADP cana-5883 282 11 quadratic quadratic ADJ cana-5883 282 12 deceleration deceleration NOUN cana-5883 282 13 parameter parameter NOUN cana-5883 282 14 , , PUNCT cana-5883 282 15 de de NOUN cana-5883 282 16 gruyter gruyter NOUN cana-5883 282 17 , , PUNCT cana-5883 282 18 https://www.degruyter.com/https://doi.org/10.1515/zna-2021-0192 https://www.degruyter.com/https://doi.org/10.1515/zna-2021-0192 NOUN cana-5883 282 19 32.bishi 32.bishi NUM cana-5883 282 20 , , PUNCT cana-5883 282 21 b. b. PROPN cana-5883 282 22 k. k. PROPN cana-5883 282 23 ,et ,et PROPN cana-5883 282 24 al al PROPN cana-5883 282 25 . . PROPN cana-5883 282 26 , , PUNCT cana-5883 282 27 2017.lrs 2017.lrs PROPN cana-5883 282 28 bianchi bianchi PROPN cana-5883 282 29 type type PROPN cana-5883 282 30 - - PUNCT cana-5883 282 31 i i PRON cana-5883 282 32 cosmological cosmological ADJ cana-5883 282 33 model model NOUN cana-5883 282 34 with with ADP cana-5883 282 35 constant constant ADJ cana-5883 282 36 deceleration deceleration NOUN cana-5883 282 37 parameter parameter NOUN cana-5883 282 38 in in ADP cana-5883 282 39 f(r f(r PROPN cana-5883 282 40 , , PUNCT cana-5883 282 41 t t NOUN cana-5883 282 42 ) ) PUNCT cana-5883 282 43 gravity gravity NOUN cana-5883 282 44 , , PUNCT cana-5883 282 45 ijgmmp ijgmmp PROPN cana-5883 282 46 d d PROPN cana-5883 282 47 1700171http://dx.doi.org/10.1142/s0219887817501584 1700171http://dx.doi.org/10.1142/s0219887817501584 NUM cana-5883 282 48 33.tiwari 33.tiwari NUM cana-5883 282 49 , , PUNCT cana-5883 282 50 r. r. PROPN cana-5883 282 51 k. k. PROPN cana-5883 282 52 beesham beesham PROPN cana-5883 282 53 , , PUNCT cana-5883 282 54 a. a. NOUN cana-5883 282 55 and and CCONJ cana-5883 282 56 shukla shukla PROPN cana-5883 282 57 , , PUNCT cana-5883 282 58 b. b. PROPN cana-5883 282 59 k. k. PROPN cana-5883 282 60 , , PUNCT cana-5883 282 61 2018.cosmological 2018.cosmological ADJ cana-5883 282 62 model model NOUN cana-5883 282 63 with with ADP cana-5883 282 64 variable variable ADJ cana-5883 282 65 deceleration deceleration NOUN cana-5883 282 66 parameter parameter NOUN cana-5883 282 67 in in ADP cana-5883 282 68 f(r f(r PROPN cana-5883 282 69 , , PUNCT cana-5883 282 70 t t NOUN cana-5883 282 71 ) ) PUNCT cana-5883 282 72 modified modify VERB cana-5883 282 73 gravity gravity NOUN cana-5883 282 74 , , PUNCT cana-5883 282 75 int.j.geom.meth.mod.phys int.j.geom.meth.mod.phy NOUN cana-5883 282 76 . . PUNCT cana-5883 283 1 15(07 15(07 NUM cana-5883 283 2 ) ) PUNCT cana-5883 284 1 1850115 1850115 NUM cana-5883 284 2 . . PUNCT cana-5883 285 1 https://doi.org/10.1142/s0219887818501153 https://doi.org/10.1142/s0219887818501153 NUM cana-5883 285 2 34.mamon 34.mamon NUM cana-5883 285 3 , , PUNCT cana-5883 285 4 a.a a.a PROPN cana-5883 285 5 . . PROPN cana-5883 285 6 and and CCONJ cana-5883 285 7 s. s. PROPN cana-5883 285 8 das das PROPN cana-5883 285 9 , , PUNCT cana-5883 285 10 2017 2017 NUM cana-5883 285 11 . . PUNCT cana-5883 286 1 a a DET cana-5883 286 2 parametric parametric ADJ cana-5883 286 3 reconstruction reconstruction NOUN cana-5883 286 4 of of ADP cana-5883 286 5 the the DET cana-5883 286 6 deceleration deceleration NOUN cana-5883 286 7 parameter parameter NOUN cana-5883 286 8 , , PUNCT cana-5883 286 9 eur eur PROPN cana-5883 286 10 . . PUNCT cana-5883 287 1 phys phy NOUN cana-5883 287 2 . . PUNCT cana-5883 288 1 j. j. PROPN cana-5883 288 2 c c PROPN cana-5883 288 3 , , PUNCT cana-5883 288 4 vol vol NOUN cana-5883 288 5 . . PROPN cana-5883 288 6 77 77 NUM cana-5883 288 7 , , PUNCT cana-5883 288 8 p. p. NOUN cana-5883 288 9 495 495 NUM cana-5883 289 1 https://doi.org/10.1140/epjc/s10052-017-5066-4 https://doi.org/10.1140/epjc/s10052-017-5066-4 PROPN cana-5883 289 2 35.akarsu 35.akarsu NUM cana-5883 289 3 , , PUNCT cana-5883 289 4 ΓΆ.and ΓΆ.and NOUN cana-5883 289 5 dereli dereli NOUN cana-5883 289 6 , , PUNCT cana-5883 289 7 t. t. PROPN cana-5883 289 8 ,2012.cosmological ,2012.cosmological PUNCT cana-5883 289 9 models model NOUN cana-5883 289 10 with with ADP cana-5883 289 11 linearly linearly ADV cana-5883 289 12 varying vary VERB cana-5883 289 13 deceleration deceleration NOUN cana-5883 289 14 parameter parameter NOUN cana-5883 289 15 , , PUNCT cana-5883 289 16 int int NOUN cana-5883 289 17 . . PUNCT cana-5883 290 1 j. j. PROPN cana-5883 290 2 theor theor PROPN cana-5883 290 3 . . PUNCT cana-5883 291 1 phys phy NOUN cana-5883 291 2 . . PUNCT cana-5883 291 3 , , PUNCT cana-5883 291 4 vol vol NOUN cana-5883 291 5 . . PROPN cana-5883 291 6 51 51 NUM cana-5883 291 7 , , PUNCT cana-5883 291 8 p. p. NOUN cana-5883 291 9 612https://doi.org/10.1007/s10773-011-0941-5 612https://doi.org/10.1007/s10773-011-0941-5 NUM cana-5883 292 1 36.bakery 36.bakery NUM cana-5883 292 2 , , PUNCT cana-5883 292 3 m.a m.a PROPN cana-5883 292 4 . . PROPN cana-5883 292 5 and and CCONJ cana-5883 292 6 shafeek shafeek PROPN cana-5883 292 7 , , PUNCT cana-5883 292 8 a.t a.t PROPN cana-5883 292 9 . . PROPN cana-5883 292 10 ,(2019 ,(2019 PROPN cana-5883 292 11 ) ) PUNCT cana-5883 292 12 . . PUNCT cana-5883 293 1 the the DET cana-5883 293 2 periodic periodic ADJ cana-5883 293 3 universe universe NOUN cana-5883 293 4 with with ADP cana-5883 293 5 varying vary VERB cana-5883 293 6 deceleration deceleration NOUN cana-5883 293 7 parameter parameter NOUN cana-5883 293 8 of of ADP cana-5883 293 9 the the DET cana-5883 293 10 second second ADJ cana-5883 293 11 degree degree NOUN cana-5883 293 12 , , PUNCT cana-5883 293 13 astrophys astrophy NOUN cana-5883 293 14 . . PUNCT cana-5883 294 1 space space PROPN cana-5883 294 2 sci sci PROPN cana-5883 294 3 . . PROPN cana-5883 294 4 , , PUNCT cana-5883 294 5 vol vol NOUN cana-5883 294 6 . . PROPN cana-5883 294 7 364 364 NUM cana-5883 294 8 , , PUNCT cana-5883 294 9 p. p. NOUN cana-5883 294 10 135 135 NUM cana-5883 294 11 https://doi.org/10.1007/s10509-019-3625-x https://doi.org/10.1007/s10509-019-3625-x PROPN cana-5883 294 12 37 37 NUM cana-5883 294 13 . . PUNCT cana-5883 294 14 tiwari tiwari PROPN cana-5883 294 15 , , PUNCT cana-5883 294 16 r.k r.k PROPN cana-5883 294 17 . . PROPN cana-5883 294 18 , , PUNCT cana-5883 294 19 et et PROPN cana-5883 294 20 al al PROPN cana-5883 294 21 . . PROPN cana-5883 294 22 ,2021 ,2021 PROPN cana-5883 294 23 . . PUNCT cana-5883 295 1 reconstruction reconstruction NOUN cana-5883 295 2 of of ADP cana-5883 295 3 models model NOUN cana-5883 295 4 with with ADP cana-5883 295 5 variable variable ADJ cana-5883 295 6 cosmological cosmological ADJ cana-5883 295 7 parameter parameter NOUN cana-5883 295 8 in in ADP cana-5883 295 9 f(r f(r PROPN cana-5883 295 10 , , PUNCT cana-5883 295 11 t t NOUN cana-5883 295 12 ) ) PUNCT cana-5883 295 13 theory theory NOUN cana-5883 295 14 , , PUNCT cana-5883 295 15 physical physical PROPN cana-5883 295 16 sciences sciences PROPN cana-5883 295 17 forum forum PROPN cana-5883 295 18 . . PUNCT cana-5883 296 1 vol vol NOUN cana-5883 296 2 . . PROPN cana-5883 297 1 2 2 NUM cana-5883 297 2 . . X cana-5883 297 3 no no INTJ cana-5883 297 4 . . NOUN cana-5883 297 5 1 1 X cana-5883 297 6 . . X cana-5883 297 7 mdpi mdpi X cana-5883 297 8 https://doi.org/10.3390/ecu2021-09372 https://doi.org/10.3390/ecu2021-09372 X cana-5883 297 9 38.tiwari 38.tiwari PROPN cana-5883 297 10 , , PUNCT cana-5883 297 11 r.k r.k PROPN cana-5883 297 12 . . PROPN cana-5883 297 13 ,et ,et PUNCT cana-5883 297 14 al al PROPN cana-5883 297 15 . . PROPN cana-5883 297 16 ,2020 ,2020 PROPN cana-5883 297 17 . . PUNCT cana-5883 298 1 international international ADJ cana-5883 298 2 journal journal PROPN cana-5883 298 3 of of ADP cana-5883 298 4 geometric geometric ADJ cana-5883 298 5 methods method NOUN cana-5883 298 6 in in ADP cana-5883 298 7 modern modern ADJ cana-5883 298 8 physics physic NOUN cana-5883 298 9 , , PUNCT cana-5883 298 10 17(12 17(12 NUM cana-5883 298 11 ) ) PUNCT cana-5883 298 12 , , PUNCT cana-5883 298 13 2050187 2050187 NUM cana-5883 298 14 . . PUNCT cana-5883 299 1 https://doi.org/10.1142/s021988782050187x https://doi.org/10.1142/s021988782050187x PROPN cana-5883 299 2 39 39 NUM cana-5883 299 3 . . PUNCT cana-5883 300 1 kumar kumar PROPN cana-5883 300 2 , , PUNCT cana-5883 300 3 r. r. PROPN cana-5883 300 4 , , PUNCT cana-5883 300 5 & & CCONJ cana-5883 300 6 arora arora PROPN cana-5883 300 7 , , PUNCT cana-5883 300 8 s. s. PROPN cana-5883 300 9 2022 2022 NUM cana-5883 300 10 . . PUNCT cana-5883 301 1 bi bi ADJ cana-5883 301 2 - - ADJ cana-5883 301 3 quadratic quadratic ADJ cana-5883 301 4 varying vary VERB cana-5883 301 5 deceleration deceleration NOUN cana-5883 301 6 parameter parameter NOUN cana-5883 301 7 to to PART cana-5883 301 8 study study VERB cana-5883 301 9 the the DET cana-5883 301 10 cosmological cosmological ADJ cana-5883 301 11 model model NOUN cana-5883 301 12 . . PUNCT cana-5883 302 1 in in ADP cana-5883 302 2 journal journal PROPN cana-5883 302 3 of of ADP cana-5883 302 4 physics physics PROPN cana-5883 302 5 : : PUNCT cana-5883 302 6 conference conference NOUN cana-5883 302 7 series series NOUN cana-5883 302 8 ( ( PUNCT cana-5883 302 9 vol vol NOUN cana-5883 302 10 . . PUNCT cana-5883 302 11 2267 2267 NUM cana-5883 302 12 , , PUNCT cana-5883 302 13 no no INTJ cana-5883 302 14 . . NOUN cana-5883 302 15 1 1 NUM cana-5883 302 16 , , PUNCT cana-5883 302 17 p. p. NOUN cana-5883 302 18 012138 012138 NUM cana-5883 302 19 ) ) PUNCT cana-5883 302 20 . . PUNCT cana-5883 303 1 iop iop PROPN cana-5883 303 2 publishing publishing NOUN cana-5883 303 3 . . PUNCT cana-5883 304 1 40 40 NUM cana-5883 304 2 . . PUNCT cana-5883 305 1 mishra mishra PROPN cana-5883 305 2 , , PUNCT cana-5883 305 3 k. k. PROPN cana-5883 305 4 r. r. PROPN cana-5883 305 5 , , PUNCT cana-5883 305 6 chaudhary chaudhary PROPN cana-5883 305 7 , , PUNCT cana-5883 305 8 h. h. PROPN cana-5883 305 9 , , PUNCT cana-5883 305 10 kumar kumar PROPN cana-5883 305 11 , , PUNCT cana-5883 305 12 r. r. PROPN cana-5883 305 13 , , PUNCT cana-5883 305 14 nekouee nekouee PROPN cana-5883 305 15 , , PUNCT cana-5883 305 16 z. z. PROPN cana-5883 305 17 , , PUNCT cana-5883 305 18 & & CCONJ cana-5883 305 19 pacif pacif PROPN cana-5883 305 20 , , PUNCT cana-5883 305 21 s. s. PROPN cana-5883 305 22 k. k. PROPN cana-5883 305 23 j. j. PROPN cana-5883 305 24 2024 2024 NUM cana-5883 305 25 . . PUNCT cana-5883 306 1 significance significance NOUN cana-5883 306 2 of of ADP cana-5883 306 3 a a DET cana-5883 306 4 quadratically quadratically ADV cana-5883 306 5 varying vary VERB cana-5883 306 6 deceleration deceleration NOUN cana-5883 306 7 parameter parameter NOUN cana-5883 306 8 in in ADP cana-5883 306 9 scalar scalar ADJ cana-5883 306 10 field field NOUN cana-5883 306 11 - - PUNCT cana-5883 306 12 dominated dominate VERB cana-5883 306 13 model model NOUN cana-5883 306 14 and and CCONJ cana-5883 306 15 cosmic cosmic ADJ cana-5883 306 16 acceleration acceleration NOUN cana-5883 306 17 . . PUNCT cana-5883 307 1 modern modern ADJ cana-5883 307 2 physics physics NOUN cana-5883 307 3 letters letter NOUN cana-5883 307 4 a a PRON cana-5883 307 5 , , PUNCT cana-5883 307 6 39(19n20 39(19n20 NUM cana-5883 307 7 ) ) PUNCT cana-5883 307 8 , , PUNCT cana-5883 307 9 2450087 2450087 NUM cana-5883 307 10 . . PUNCT cana-5883 308 1 41.berman 41.berman NUM cana-5883 308 2 , , PUNCT cana-5883 308 3 m. m. NOUN cana-5883 308 4 s. s. PROPN cana-5883 308 5 1983 1983 NUM cana-5883 308 6 . . PUNCT cana-5883 309 1 a a DET cana-5883 309 2 special special ADJ cana-5883 309 3 law law NOUN cana-5883 309 4 of of ADP cana-5883 309 5 variation variation NOUN cana-5883 309 6 for for ADP cana-5883 309 7 hubble’sparameter hubble’sparameter ADJ cana-5883 309 8 , , PUNCT cana-5883 309 9 il il PROPN cana-5883 309 10 nuovo nuovo PROPN cana-5883 309 11 cimento cimento PROPN cana-5883 309 12 b b PROPN cana-5883 309 13 ( ( PUNCT cana-5883 309 14 1971 1971 NUM cana-5883 309 15 - - SYM cana-5883 309 16 1996 1996 NUM cana-5883 309 17 ) ) PUNCT cana-5883 309 18 , , PUNCT cana-5883 309 19 vol vol NOUN cana-5883 309 20 . . PROPN cana-5883 309 21 74 74 NUM cana-5883 309 22 , , PUNCT cana-5883 309 23 no no INTJ cana-5883 309 24 . . PUNCT cana-5883 310 1 2,pp 2,pp X cana-5883 310 2 . . PUNCT cana-5883 311 1 182βˆ’186 182βˆ’186 NUM cana-5883 311 2 .. .. SYM cana-5883 311 3 https://doi.org/10.1007 https://doi.org/10.1007 ADJ cana-5883 311 4 / / SYM cana-5883 311 5 bf02721676 bf02721676 NOUN cana-5883 311 6 42.berman 42.berman NUM cana-5883 311 7 , , PUNCT cana-5883 311 8 m. m. NOUN cana-5883 311 9 s. s. PROPN cana-5883 311 10 and and CCONJ cana-5883 311 11 gomide gomide PROPN cana-5883 311 12 , , PUNCT cana-5883 311 13 f. f. PROPN cana-5883 311 14 de de PROPN cana-5883 311 15 mello,1988.cosmological mello,1988.cosmological ADJ cana-5883 311 16 models model NOUN cana-5883 311 17 with with ADP cana-5883 311 18 constant constant ADJ cana-5883 311 19 deceleration deceleration NOUN cana-5883 311 20 parameter parameter NOUN cana-5883 311 21 , , PUNCT cana-5883 311 22 gen gen PROPN cana-5883 311 23 . . PROPN cana-5883 311 24 relat relat PROPN cana-5883 311 25 . . PUNCT cana-5883 312 1 gravit gravit PROPN cana-5883 312 2 . . PUNCT cana-5883 313 1 ,vol ,vol PROPN cana-5883 313 2 . . PUNCT cana-5883 314 1 20 20 NUM cana-5883 314 2 , , PUNCT cana-5883 314 3 p. p. NOUN cana-5883 314 4 191https://doi.org/10.1007/bf00759327 191https://doi.org/10.1007/bf00759327 NUM cana-5883 315 1 43.farooq 43.farooq NUM cana-5883 315 2 , , PUNCT cana-5883 315 3 o. o. PROPN cana-5883 315 4 , , PUNCT cana-5883 315 5 madiyar madiyar PROPN cana-5883 315 6 , , PUNCT cana-5883 315 7 f. f. PROPN cana-5883 315 8 r. r. PROPN cana-5883 315 9 , , PUNCT cana-5883 315 10 crandall crandall PROPN cana-5883 315 11 , , PUNCT cana-5883 315 12 s. s. PROPN cana-5883 315 13 , , PUNCT cana-5883 315 14 & & CCONJ cana-5883 315 15 ratra ratra PROPN cana-5883 315 16 , , PUNCT cana-5883 315 17 b. b. PROPN cana-5883 315 18 ,2016 ,2016 PROPN cana-5883 315 19 . . PUNCT cana-5883 316 1 hubble hubble PROPN cana-5883 316 2 parameter parameter PROPN cana-5883 316 3 measurement measurement NOUN cana-5883 316 4 constraints constraint NOUN cana-5883 316 5 on on ADP cana-5883 316 6 the the DET cana-5883 316 7 redshift redshift NOUN cana-5883 316 8 of of ADP cana-5883 316 9 the the DET cana-5883 316 10 deceleration deceleration NOUN cana-5883 316 11 – – PUNCT cana-5883 316 12 acceleration acceleration NOUN cana-5883 316 13 transition transition NOUN cana-5883 316 14 , , PUNCT cana-5883 316 15 dynamical dynamical ADJ cana-5883 316 16 dark dark ADJ cana-5883 316 17 energy energy NOUN cana-5883 316 18 , , PUNCT cana-5883 316 19 and and CCONJ cana-5883 316 20 space space NOUN cana-5883 316 21 curvature curvature NOUN cana-5883 316 22 . . PUNCT cana-5883 317 1 the the DET cana-5883 317 2 astrophysical astrophysical ADJ cana-5883 317 3 journal journal NOUN cana-5883 317 4 , , PUNCT cana-5883 317 5 835(1 835(1 NUM cana-5883 317 6 ) ) PUNCT cana-5883 317 7 , , PUNCT cana-5883 317 8 26.doi 26.doi PROPN cana-5883 317 9 10.3847/15384357/835/1/26 10.3847/15384357/835/1/26 PROPN cana-5883 317 10 44.mahichi 44.mahichi NUM cana-5883 317 11 , , PUNCT cana-5883 317 12 e. e. PROPN cana-5883 317 13 , , PUNCT cana-5883 317 14 amani amani PROPN cana-5883 317 15 , , PUNCT cana-5883 317 16 a. a. PROPN cana-5883 317 17 , , PUNCT cana-5883 317 18 & & CCONJ cana-5883 317 19 ramzanpour ramzanpour NOUN cana-5883 317 20 , , PUNCT cana-5883 317 21 m. m. NOUN cana-5883 317 22 a. a. PROPN cana-5883 317 23 ,2021 ,2021 PROPN cana-5883 317 24 . . PUNCT cana-5883 318 1 viscous viscous ADJ cana-5883 318 2 interaction interaction NOUN cana-5883 318 3 and and CCONJ cana-5883 318 4 stability stability NOUN cana-5883 318 5 on on ADP cana-5883 318 6 dark dark ADJ cana-5883 318 7 matter matter NOUN cana-5883 318 8 bose bose NOUN cana-5883 318 9 – – PUNCT cana-5883 318 10 einstein einstein NOUN cana-5883 318 11 condensation condensation NOUN cana-5883 318 12 with with ADP cana-5883 318 13 modified modify VERB cana-5883 318 14 chaplygin chaplygin NOUN cana-5883 318 15 gas gas NOUN cana-5883 318 16 . . PUNCT cana-5883 319 1 canadian canadian ADJ cana-5883 319 2 journal journal PROPN cana-5883 319 3 of of ADP cana-5883 319 4 physics physics PROPN cana-5883 319 5 , , PUNCT cana-5883 319 6 99(11 99(11 NUM cana-5883 319 7 ) ) PUNCT cana-5883 319 8 , , PUNCT cana-5883 319 9 991-997.https://doi.org/10.1139/cjp-2021-0111 991-997.https://doi.org/10.1139/cjp-2021-0111 PROPN cana-5883 319 10 https://www.degruyter.com/ https://www.degruyter.com/ X cana-5883 319 11 https://doi.org/10.1515/zna-2021-0192 https://doi.org/10.1515/zna-2021-0192 PROPN cana-5883 319 12 http://dx.doi.org/10.1142/s0219887817501584 http://dx.doi.org/10.1142/s0219887817501584 PROPN cana-5883 319 13 https://doi.org/10.1142/s0219887818501153 https://doi.org/10.1142/s0219887818501153 PROPN cana-5883 319 14 https://doi.org/10.1007/s10773-011-0941-5 https://doi.org/10.1007/s10773-011-0941-5 NUM cana-5883 319 15 https://doi.org/10.1007/s10509-019-3625-x https://doi.org/10.1007/s10509-019-3625-x PROPN cana-5883 319 16 https://doi.org/10.3390/ecu2021-09372 https://doi.org/10.3390/ecu2021-09372 PROPN cana-5883 319 17 https://doi.org/10.1142/s021988782050187x https://doi.org/10.1142/s021988782050187x PROPN cana-5883 319 18 https://doi.org/10.1007/bf02721676 https://doi.org/10.1007/bf02721676 PROPN cana-5883 319 19 https://doi.org/10.1007/bf00759327 https://doi.org/10.1007/bf00759327 PROPN cana-5883 319 20 https://doi.org/10.1139/cjp-2021-0111 https://doi.org/10.1139/cjp-2021-0111 PROPN